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Thinking and Reasoning

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Positive Psychology
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Human Strengths
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Thinking and Reasoning
Cognitive Illusions and Fallacies


Thinking and Reasoning: A Reader's Guide (Cambridge Handbook of Thinking and Reasoning, 2005) K. Holyoak, R. Morrison
Similarity (Cambridge Handbook of Thinking and Reasoning, 2005) R. Goldstone, J. Son
The Problem of Induction (Cambridge Handbook of Thinking and Reasoning, 2005) S. Sloman, D. Lagnado
Analogy (Cambridge Handbook of Thinking and Reasoning, 2005) K. Holyoak
Deductive Reasoning (Cambridge Handbook of Thinking and Reasoning, 2005) J. Evans
Decision Making (Cambridge Handbook of Thinking and Reasoning, 2005) R. LeBoeuf, E. Shafir
A Model of Heuristic Judgment (Cambridge Handbook of Thinking and Reasoning, 2005) D. Kahneman, S. Frederick
Motivated Thinking (Cambridge Handbook of Thinking and Reasoning, 2005) D. Molden, E. Higgins
Problem Solving (Cambridge Handbook of Thinking and Reasoning, 2005) L. Novick, M. Bassok
Complex Declarative Learning (Cambridge Handbook of Thinking and Reasoning, 2005) M. Chi, S. Ohlsson
Legal Reasoning (Cambridge Handbook of Thinking and Reasoning, 2005) P. Ellsworth
Scientific Thinking and Reasoning (Cambridge Handbook of Thinking and Reasoning, 2005) K. Dunbar, J. Fugelsang
Learning To Think: Challenges of Teaching Thinking (Cambridge Handbook of Thinking and Reasoning, 2005) R. Ritchhart, D. Perkins
Practical Aspects of Theoretical Reasoning (Oxford Handbook of Rationality, 2004) G. Harman
Rationality and Psychology (Oxford Handbook of Rationality, 2004) R. Samuels, S. Stich
Rationality and Science (Oxford Handbook of Rationality, 2004) P. Thagard
Educators and Expertise: A Brief History of Theories and Models (Cambridge Handbook of Expertise and Expert Performance, 2006) R. Amirault, R. Branson
Tacit Knowledge, Practical Intelligence, and Expertise (Cambridge Handbook of Expertise and Expert Performance, 2006) A. Cianciolo, R. Sternberg
The Influence of Experience and Deliberate Practice (Cambridge Handbook of Expertise and Expert Performance, 2006) K. Ericsson
Defining and Describing Reason (The Nature of Reasoning, 2004) J. Leighton
Teaching Reasoning (The Nature of Reasoning, 2004) R. Nickerson
What Do We Know About The Nature of Reasoning? (The Nature of Reasoning, 2004) R. Sternberg
What is Induction and Why Study It? (Inductive Reasoning, 2007) E. Heit
Abductive Inference: From Philosophical Analysis to Neural Mechanisms (Inductive Reasoning, 2007) P. Thagard
The Place of Analogy in Cognition (The Analogical Mind, 2001) K. Holyoak, D. Gentner, B. Kokinov
Emotional Analogies and Analogical Inference (The Analogical Mind, 2001) P. Thagard, C. Shelley
Reasoning: Philosophical Foundations (Reasoning: Studies of Human Inference and Its Foundations, 2008) J. Adler
Inductive Logic and Inductive Reasoning (Reasoning: Studies of Human Inference and Its Foundations, 2008) H. Kyburg
Reasoning, Decision Making, and Rationality (Reasoning: Studies of Human Inference and Its Foundations, 2008) J. Evans, D. Over, K. Manktelow
Causal Thinking (Reasoning: Studies of Human Inference and Its Foundations, 2008) L. Rips


Thinking and Reasoning: A Reader's Guide, K. Holyoak, R. Morrison

It is thinking, not language, that lies closest to the core of our individual identity. A person who loses language but can still make intelligent decisions, as demonstrated by actions, is viewed as mentally intact. In contrast, the kinds of brain damage that rob an individual of the capacity to think and reason are considered the harshest blows that can be struck against a sense of personhood.

Thinking is the systematic transformation of mental representations of knowledge to characterize actual or possible states of the world, often in service of goals. Obviously, our definition introduces a plethora of terms with meanings that beg to be unpacked, but at which we can only hint. A mental representation of knowledge is an internal description that can be manipulated to form other descriptions. To count as thinking, the manipulations must be systematic transformations governed by certain constraints. Whether a logical deduction or a creative leap, what we mean by thinking is more than unconstrained associations. The internal representations created by thinking describe states of some external world (a world that may include the thinker as an object of self-reflection) – that world might be our everyday one, or perhaps some imaginary construction obeying the “laws” of magical realism. Often (not always – the daydreamer, and indeed the night dreamer, are also thinkers), thinking is directed toward achieving some desired state of affairs, some goal that motivates the thinker to perform mental work.

The study of thinking includes several interrelated subfields that reflect slightly different perspectives on thinking. Reasoning, which has a long tradition that springs from philosophy and logic, places emphasis on the process of drawing inferences (conclusions) from some initial information (premises). In standard logic, an inference is deductive if the truth of the premises guarantees the truth of the conclusion by virtue of the argument form. If the truth of the premises renders the truth of the conclusion more credible but does not bestow certainty, the inference is called inductive. Judgment and decision making involve assessment of the value of an option or the probability that it will yield a certain payoff (judgment) coupled with choice among alternatives (decision making). Problem solving involves the construction of a course of action that can achieve a goal.

Before psychology was founded, the eighteenth-century philosophers Immanuel Kant (in Germany) and David Hume (in Scotland) laid the foundations for all subsequent work on the origins of causal knowledge, perhaps the most central problem in the study of thinking. If we were to choose one phrase to set the stage for modern views of thinking, it would be an observation of the British philosopher Thomas Hobbes, who, in 1651 , in his treatise Leviathan, proposed, “Reasoning is but reckoning.” “Reckoning” is an odd term today, but in the seventeenth century it meant computation, as in arithmetic calculations.

The modern conception of thinking as computation became prominent in the 1970s. In their classic treatment of human problem solving, Allen Newell and Herbert Simon showed that the computational analysis of thinking (anticipated by Alan Turing, the father of computer science) could yield important empirical and theoretical results. Like a program running on a digital computer, a person thinking through a problem can be viewed as taking an input that represents initial conditions and a goal, and applying a sequence of operations to reduce the difference between the initial conditions and the goal.

Similarity, R. Goldstone, J. Son

Human assessments of similarity are fundamental to cognition because similarities in the world are revealing. The world is an orderly enough place that similar objects and events tend to behave similarly. This fact of the world is not just a fortunate coincidence. It is because objects are similar that they will tend to behave similarly in most respects. It is because crocodiles and alligators are similar in their external form, internal biology, behavior, diet, and customary environment that one can often successfully generalize from what one knows of one to the other. As Quine observed, “Similarity, is fundamental for learning, knowledge and thought, for only our sense of similarity allows us to order things into kinds so that these can function as stimulus meanings. Reasonable expectation depends on the similarity of circumstances and on our tendency to expect that similar causes will have similar effects”. Similarity thus plays a crucial role in making predictions because similar things usually behave similarly.

As the similarity between A and B increases, so does the probability of correctly inferring that B has X upon knowing that A has X. This relation assumes we have no special knowledge related to property X. Empirically, Heit and Rubinstein showed that if we do know about the property, then this knowledge, rather than a one-size-fits-all similarity, is used to guide our inferences.

We tend to rely on similarity to generate inferences and categorize objects into kinds when we do not know exactly what properties are relevant or when we cannot easily separate an object into separate properties. Similarity is an excellent example of a domain-general source of information. Even when we do not have specific knowledge of a domain, we can use similarity as a default method to reason about it. The contravening limitation of this domain generality is that when specific knowledge is available, then a generic assessment of similarity is no longer as relevant.

If an event is similar enough to a previously experienced event, the stored event’s outcome may be offered as a candidate prediction for the current event. If an unknown object is similar enough to a known object, then the known object’s category label may be applied to the unknown object. The act of comparing events, objects, and scenes and establishing similarities between them is of critical importance for the cognitive processes we depend on.

Another reason for studying similarity is that it provides an elegant diagnostic tool for examining the structure of our mental entities and the processes that operate on them. For example, one way to tell that a physicist has progressed beyond the novice stage is that he or she sees deep similarities between problems that require calculation of force even though the problems are superficially dissimilar.

The study of similarity is typically justified by the argument that so many theories in cognition depend on similarity as a theoretical construct. An account of what makes problems, memories, objects, and words similar to one another often provides the backbone for our theories of problem solving, attention, perception, and cognition. As William James put it, “This sense of Sameness is the very keel and backbone of our thinking”.

People seem to have difficulty ignoring similarities between old and new patterns even when they know a straightforward and perfectly accurate categorization rule. There may be a mandatory consideration of similarity in many categorization judgments, adding constraints to categorization. At the same time, similarity may be more flexible and sophisticated than commonly acknowledged and this may also serve to bridge the gap between similarity and highlevel cognition. Krumhansl argued that similarity between objects decreases when they are surrounded by many close neighbors that were also presented on previous trials.

Similarity judgments not only depend on the context established by recently exposed items, simultaneously presented items, and inferred contrast sets, but also on the observer. Suzuki, Ohnishi, and Shigemasu showed that similarity judgments depend on level of expertise and goals. Expert and novice subjects were asked to solve the Tower of Hanoi puzzle and judge the similarity between the goal and various states. Experts’ similarity ratings were based on the number of moves required to transform one position to the other. Less expert subjects tended to base their judgments on the number of shared superficial features.

The skeptic might now believe that similarity is much too flexible to be a stable ground for cognition. In fact, Nelson Goodman put forth exactly this claim, maintaining that the notion of similarity is either vague or unnecessary. He argued that “when to the statement that two things are similar we add a specification of the property that they have in common . . . we render it [the similarity statement] superfluous”. That is, all the potential explanatory work is done by the “with respect to property Z” clause and not by the similarity statement.

In most cases, similarity is useful precisely because we cannot flesh out the “respect to property Z” clause with just a single property. Evidence suggests that assessments of overall similarity are natural and perhaps even “primitive.” Evidence from children’s perception of similarity suggests that children are particularly likely to judge similarity on the basis of many integrated properties rather than analysis into dimensions. Even dimensions that are perceptually separable are treated as fused in similarity judgments.

There is also evidence that adults often have an overall impression of similarity without analysis into specific properties. Ward found that adult subjects who tended to group objects quickly also tended to group objects like children by considering overall similarity across all dimensions instead of maximal similarity on one dimension.

A corollary of this contention is that our default impression of similarity does not typically mislead us; it is explicitly designed to lead us to see relations between things that often function similarly in our world. People, with good reason, expect their default similarity assessments to provide good clues about where to uncover directed, nonapparent similarities.

A possible conclusion is that similarity is not a coherent notion at all. The term similarity, similar to 'family values', may not pick out a consolidated or principled set of things. Although we sympathize with the impulse toward domain-specific accounts of similarity, we also believe in the value of studying general principles of comparison that potentially underlie many domains. Although we do not know whether general principles exist, one justification for pursuing them is the large payoff that would result from discovering these principles if they do exist. A historically fruitful strategy, exemplified by Einstein’s search for a law to unify gravitational and electromagnetic acceleration and Darwin’s search for a unified law to understand the origins of humans and other animals, has been to understand differences as parametric variations within a single model. Finding differences across tasks does not necessarily point to the incoherency of similarity. An alternative perspective would use these task differences as an illuminating source of information in developing a unified account.

The Problem of Induction, S. Sloman, D. Lagnado

In its classic formulation, due to Hume, inductive reasoning is an activity of the mind that takes us from the observed to the unobserved. From the fact that the sun has risen every day thus far, we conclude that it will rise again tomorrow; from the fact that bread has nourished us in the past, we conclude that it will nourish us in the future. The essence of inductive reasoning lies in its ability to take us beyond the confines of our current evidence or knowledge to novel conclusions about the unknown. These conclusions may be particular, as when we infer that the next swan we see will be white, or general, as when we infer that all swans are white. They may concern the future, as in the prediction of rain from a dark cloud, or concern something in the past, as in the diagnosis of an infection from current symptoms.

Hume argued that all such reasoning is founded on the relation of cause and effect. It is this relation that takes us beyond our current evidence, whether it is an inference from cause to effect, or effect to cause, or from one collateral effect to another. Having identified the causal basis of our inductive reasoning, Hume proceeded to raise a fundamental question now known as “the problem of induction” – what are the grounds for such inductive or causal inferences? In attempting to answer this question, Hume presents both a negative and a positive argument. In his negative thesis, Hume argued that our knowledge of causal relations is not attainable through demonstrative reasoning, but is acquired through past experience. To illustrate, our belief that fire causes heat, and the expectation that it will do so in the future, is based on previous cases in which one has followed the other, and not on any a priori reasoning. However, once Hume identified experience as the basis for inductive inference, he proceeded to demonstrate its inadequacy as a justification for these inferences. Put simply, any such argument requires the presupposition that past experience will be a good guide to the future, and this is the very claim we seek to justify.

For Hume, what is critical about our experience is the perceived similarity between particular causes and their effects: “From causes, which appear similar, we expect similar effects. This is the sum of all our experimental conclusions”. However, this expectation cannot be grounded in reason alone because similar causes could conceivably be followed by dissimilar effects. Moreover, if one introduces hidden powers or mechanisms to explain our observations at a deeper level, the problem just gets shifted down. What guarantees that the powers or mechanisms that underlie our current experiences will do so in the future? In short, Hume’s negative argument undermines the assumption that the future will resemble the past. This assumption cannot be demonstrated a priori because it is not contradictory to imagine that the course of nature may change. However, neither can it be supported by an appeal to past experience because this would be to argue in a circle.

Hume’s positive argument provides an answer to the descriptive question of how we actually pass from the unobserved to the observed but not to the justificatory one. He argues that it is custom or habit that leads us to make inferences in accordance with past regularities. Thus, after observing many cases of a flame being accompanied by heat, a novel instance of a flame creates the idea, and hence an expectation, of heat. In this way, a correspondence is set up between the regularities in the world and the expectations of the mind. Moreover, Hume maintains that this tendency is “implanted in us as an instinct” because nature would not entrust it to the vagaries of reason. In modern terms, then, we are prewired to expect past associations to hold in the future, although what is associated with what will depend on the environment we experience. This idea of a general-purpose associative learning system has inspired many contemporary accounts of inductive learning.

If we are to acquire any predictive habits, we must be able to generalize to some extent from one object to another, or to the same object at different times and contexts. How this is carried out is as much in need of a descriptive account as the problem of induction itself. Second, we might accept that no reflective reasoning can justify our inductive inferences, but this does not entail that reflective reasoning cannot be the actual cause of some of our inferences. Nevertheless, Hume presciently identified the critical role of both similarity and causality in inductive reasoning, the variables that, as we will see, are at the heart of work on the psychology of induction.

Goodman’s problem of projectibility concerns how we distinguish projectible predicates such as “green” from nonprojectible ones such as “grue.” Although he concurred with Hume’s claim that induction consists of a mental habit formed by past regularities, he argued that Hume overlooked the further problem (the new riddle) of which past regularities are selected by this mental habit and thus projected in the future. After all, it would appear that we experience a vast range of regularities and yet are prepared to project only a small subset. Goodman himself offered a solution in terms of entrenchment. In short, a predicate is entrenched if it has a past history of use, where both the term itself, and the extension of the term, figure in this usage. Thus, “green” is entrenched, whereas “grue” is not because our previous history of projections involves numerous cases of the former, but none of the latter. In common with Hume, then, Goodman gave a descriptive account of inductive inference, but one grounded in the historic practices of people, and in particular their language use, rather than simply the psychology of an individual.

In his essay, “Natural Kinds”, Quine defended a simple and intuitive answer to Goodman’s problem: Projectible predicates apply to members of a kind, a grouping formed on the basis of similarity. Thus, “green” is projectible, whereas “grue” is not because green things are more similar than grue things; that is, green emeralds form a kind, whereas grue emeralds do not. This shifts the explanatory load onto the twin notions of similarity and kind, which Quine held to be fundamental to inductive inference: “every reasonable expectation depends on similarity.” For Quine, both humans and animals possess an innate standard of similarity useful for making appropriate inductions.Without this prior notion, no learning or generalization can take place. Despite the subjectivity of this primitive similarity standard, Quine believed that its uniformity across humans makes the inductive learning of verbal behavior relatively straightforward. What guarantees, however, that our “innate subjective spacing of qualities” matches up with appropriate groupings in nature? Here, Quine appealed to an evolutionary explanation: Without such a match, and thus the ability to make appropriate inductions, survival is unlikely.

For Quine, our notions of similarity and the way in which we group things become increasingly sophisticated and abstract, culminating, he believed, in their eventual removal from mature science altogether. This conclusion seems to sit uneasily with his claims about theoretical similarity. Nevertheless, as mere humans, we will always be left with a spectrum of similarity notions and systems of kinds applicable as the context demands, which accounts for the coexistence of a variety of procedures for carrying out inductive inference, a plurality that appears to be echoed in more recent cognitive psychology.

Many predicates that people reason about are emergent properties whose existence depends on the attitude of a reasoning agent (consider “is beautiful” or a cloud that “looks like a mermaid”). So we cannot simply represent predicates as functions of simpler perceptual properties. Something else is needed, something that respects the information we have about predicates via the relations of objects and predicates to one another.

Tversky proposed a new measure that posited that similarity could be computed over a large number of dimensions, that both common and distinctive features were essential to determine the similarity between any pair of objects, and, critically, that the set of features used to measure similarity were context dependent. Features depended on their diagnosticity in the set of objects being compared and on the specific task used to measure similarity. Tversky’s contrast model of similarity would, it was hoped, prove to have sufficient representational power to model a number of cognitive tasks, including categorization and induction.

The representativeness heuristic is essentially the idea that categorical knowledge is used to make probability judgments. In that sense, it is an extension of Rosch’s insights about category structure. She showed that similarity was a guiding principle in decisions about category membership; Kahneman and Tversky showed that probability judgment could, in some cases, be understood as a process of categorization driven by similarity.

To limit the scope of this chapter, in the remainder we focus exclusively on the psychology of categorical induction: How people arrive at a statement of their confidence that a conclusion category has a predicate after being told that one or more premise categories do. As Goodman’s analysis makes clear, this is a very general problem.

The general question will be how people go about determining their belief in the conclusion of such an argument after being told that the premises are true.We discuss this question both by trying to describe human judgment as a set of phenomena and by trying to explain the existence of these phenomena in terms of more fundamental and more general principles. The phenomena will concern judgments of the strength of categorical arguments or the convincingness of an argument or some other measure of belief in the conclusion once the premises are given.

Perhaps the most obvious and robust predictor of inductive strength is similarity. In the simplest case, most people are willing to project a property known to be true of (say) crocodiles to a very similar class, such as alligators, with some degree of confidence. Such willingness exists either because similarity is a mechanism of induction or because induction and similarity judgment have some common antecedent. From the scores of examples of the representativeness heuristic at work through Rosch’s analysis of typicality in terms of similarity, a strong correlation between probability and similarity is more the rule than the exception. The argument has been made that similarity is not a real explanation at all and phenomena exist that contradict prediction based only on similarity. Nevertheless, similarity remains the key construct in the description and explanation of inductive phenomena.

Similarity

Arguments are strong to the extent that categories in the premises are similar to the conclusion category. For example, Robins have sesamoid bones. Therefore, sparrows have sesamoid bones. is judged stronger than Robins have sesamoid bones. Therefore, ostriches have sesamoid bones. because robins are more similar to sparrows than to ostriches.

Typicality

The more typical premise categories are of the conclusion category, the stronger is the argument. For example, people are more willing to project a predicate from robins to birds than from penguins to birds because robins are more typical birds than penguins.

Osherson et al. posited the similaritycoverage model that proposed that people make categorical inductions on the basis of two principles, similarity and category coverage. Category coverage was actually cashed out in terms of similarity. According to the model, arguments are deemed strong to the degree that premise and conclusion categories are similar and to the degree that premises “cover” the lowest-level category that includes both premise and conclusion categories. The idea is that the categories present in the argument elicit their common superordinate – in particular, the most specific superordinate that they share. Category coverage is determined by the similarity between the premise categories and all the categories contained in this lowest-level superordinate.

Asymmetry

Switching premise and conclusion categories can lead to arguments of different strength: Tigers have 38 chromosomes. Therefore, buffaloes have 38 chromosomes. is judged stronger than Buffaloes have 38 chromosomes. Therefore, tigers have 38 chromosomes.

Diversity

The less similar premises are to each other, the stronger the argument tends to be. People are more willing to draw the conclusion that all mammals love onions from the fact that hippos and hamsters love onions than from the fact that hippos and rhinos do because hippos and rhinos are more similar than hippos and hamsters.

Feature exclusion

A premise category that has little overlap with the conclusion category should have no effect on argument strength even if it leads to a more diverse set of premises. For example, Fact: German Shepherds have sesamoid bones. Fact: Giraffes have sesamoid bones. Conclusion: Moles have sesamoid bones. is judged stronger than Fact: German Shepherds have sesamoid bones. Fact: Blue whales have sesamoid bones. Conclusion: Moles have sesamoid bones.

Monotonicity and Nonmonotonicity

When premise categories are sufficiently similar, adding a supporting premise will increase the strength of an argument. However, a counterexample to monotonicity occurs when a premise with a category dissimilar to all other categories is introduced: Crows have strong sternums. Peacocks have strong sternums. Therefore, birds have strong sternums. is stronger than Crows have strong sternums. Peacocks have strong sternums. Rabbits have strong sternums. Therefore, birds have strong sternums.

Inclusion Fallacy

Similarity relations can override categorical relations between conclusions. Most people judge All robins have sesamoid bones. Therefore, all birds have sesamoid bones. to be stronger than All robins have sesamoid bones. Therefore, all ostriches have sesamoid bones.

Inclusion Similarity

Similarity relations can override even transparent categorical relations between premise and conclusion. People do not always judge Every individual body of water has a high number of seiches. Every individual lake has a high number of seiches. to be perfectly strong even when they agree that a lake is a body ofwater. Moreover, they judge Every individual body of water has a high number of seiches. Every individual reservoir has a high number of seiches. to be even weaker, presumably because reservoirs are less typical bodies of water than lakes.

Naming effect

Children prefer to project predicates between objects that look similar rather than objects that look dissimilar. However, this preference is overridden when the dissimilar objects are given similar labels.

Preferred level of induction

People are willing to make an inductive inference with confidence from a subordinate to a near superordinate up to the folk-generic level; their willingness drops off considerably when making inferences to categories more abstract.

Coley et al.’s answer to the 'naming' conundrum is that naming depends on knowledge; that is, names are chosen that are precise enough to be informative given what people know about the object being named. Inductive inference, they argued, also depends on a kind of conventional wisdom. People have learned to maximize inductive potential at a particular level of generality (the folk-generic) level because culture and linguistic convention specify that that is the most informative level for projecting properties. For example, language tends to use a single morpheme for naming generic level categories. This is a powerful cue that members of the same generic level have a lot in common and that therefore it is a good level for guessing that a predicate might hold across it. This idea is related to Shipley’s notion of overhypotheses: that people use categorywide rules about certain kinds of properties to make some inductive inferences. For example, upon encountering a new species, people might assume members of the species will vary more in degree of obesity than in, say, skin color despite having no particular knowledge about the species.

This observation poses a challenge to feature- and similarity-based models of induction. These models all start from the assumption that people induce new knowledge about categories from old knowledge about the same categories. However, if people make inductive inferences using not only specific knowledge about the categories at hand but also distributional knowledge about the likelihood of properties at different hierarchical levels, knowledge that is in part culturally transmitted via language, then more enters the inductive inference process than models of inductive process have heretofore allowed.

Induction is of course not merely the province of individuals trying to accomplish everyday goals, but also one of the main activities of science. According to one common view of science, scientists spend much of their time trying to induce general laws about categories from particular examples. It is natural, therefore, to look to the principles that govern induction in science to see how well they describe individual behavior. Psychologists have approached induction as a scientific enterprise in three different ways.

Variability/Centrality

People are more willing to project predicates that tend to be invariant across category instances than variable predicates. For example, people who are told that one Pacific island native is overweight tend to think it is unlikely that all natives of the island are overweight because weight tends to vary across people. In contrast, if told the native has dark skin, they are more likely to generalize to all natives because skin color tends to be more uniform within a race.

Human bias

Small children prefer to project a property from people rather than from other animals. Four-year-olds are more likely to agree that a bug has a spleen if told that a person does than if told that a bee does. Ten-year-olds and adults do not show this asymmetry and project as readily from nonhuman animals as from humans.

Induction as Hypothesis Evaluation Mc- Donald, Samuels, and Rispoli proposed an account of inductive inference that appeals to several principles of hypothesis evaluation. They argued that when judging the strength of an inductive argument, people actively construct and assess hypotheses in light of the evidence provided by the premises. They advanced three determinants of hypothesis plausibility: the scope of the conclusion, the number of premises that instantiate it, and the number of alternatives to it suggested by the premises. In their experiments, all three factors were good predictors of judged argument strength, although certain pragmatic considerations, and a fourth factor – “acceptability of the conclusion” – were also invoked to fully cover the results.

Inductive inference can be fallacious, as demonstrated by the inclusion fallacy described previously. Nevertheless, much of the evidence that has been covered in this section suggests that people in the psychologist’s laboratory are sensitive to some of the same concerns as scientists when they make inductive inferences. People are more likely to project nonvariable over variable predicates, they change their beliefs more when premises are a priori less likely, and their behavior can be modeled by probabilistic models constructed from rational principles.

Kahneman and Tversky have suggested that people use a set of cognitive heuristics to estimate probabilities – heuristics that were informed, that made people’s estimates likely to be reasonable, but left open the possibility of systematic error in cases in which the heuristics that came naturally to people had the unfortunate consequence of leading to the wrong answer. Kahneman and Tversky suggested the heuristics of availability, anchoring and adjustment, simulation, and causality to describe how people make probability judgments. They also suggested that people make judgments according to representativeness, the degree to which a class or event used as evidence is similar to the class or process being judged.

Relevance

People’s willingness to project a predicate from one category to another depends on what else the two categories have in common. For example, people are more likely to project “has a liver with two chambers” from chickens to hawks than from tigers to hawks but more likely to project “prefers to feed at night” from tigers to hawks than from chickens to hawks.

Causal asymmetry

Switching premise and conclusion categories will reduce the strength of an argument if a causal path exists from premise to conclusion. For example, Gazelles contain retinum. Lions contain retinum. is stronger than Lions contain retinum. Gazelles contain retinum. because the food chain is such that lions eat gazelles and retinum could be transferred in the process.

Organisms have a striking ability to find the properties of things that maximize their ability to predict and control, and humans seem to have the most widely applicable capacity of this sort. However, prediction and control come from knowing what variables determine the values of other variables – that is, how one predicts future outcomes and knows what to manipulate to achieve an effect. This is, of course, the domain of causality. It seems only natural that people would use this talent to reason when making inductive inferences.

Analogy, K. Holyoak

Analogy is a special kind of similarity. Two situations are analogous if they share a common pattern of relationships among their constituent elements even though the elements themselves differ across the two situations. Typically, one analog, termed the source or base, is more familiar or better understood than the second analog, termed the target. This asymmetry in initial knowledge provides the basis for analogical transfer, using the source to generate inferences about the target. For example, Charles Darwin drew an analogy between breeding programs used in agriculture to select more desirable plants and animals and “natural selection” for new species. The well-understood source analog called attention to the importance of variability in the population as the basis for change in the distribution of traits over successive generations and raised a critical question about the target analog: What plays the role of the farmer in natural selection?

Analogies have figured prominently in the history of science and mathematics and are of general use in problem solving. In legal reasoning, the use of relevant past cases (legal precedents) to help decide a new case is a formalized application of analogical reasoning. Analogies can also function to influence political beliefs and to sway emotions. Analogical reasoning goes beyond the information initially given, using systematic connections between the source and target to generate plausible, although fallible, inferences about the target. Analogy is thus a form of inductive reasoning.

Typically, a target situation serves as a retrieval cue for a potentially useful source analog. It is then necessary to establish a mapping, or a set of systematic correspondences that serve to align the elements of the source and target. On the basis of the mapping, it is possible to derive new inferences about the target, thereby elaborating its representation. In the aftermath of analogical reasoning about a pair of cases, it is possible that some form of relational generalization may take place, yielding a more abstract schema for a class of situations, of which the source and target are both instances. For example, Darwin’s use of analogy to construct a theory of natural selection ultimately led to the generation of a more abstract schema for a selection theory, which in turn helped to generate new specific theories in many fields, including economics, genetics, sociobiology, and artificial intelligence. Analogy is one mechanism for effecting conceptual change.

Lakoff and Johnson argued that much of human experience, especially its abstract aspects, is grasped in terms of broad conceptual metaphors (e.g., events occurring in time are understood by analogy to objects moving in space). Time, for example, is understood in terms of objects in motion through space as in expressions such as “My birthday is fast approaching” and “The time for action has arrived.” As Lakoff and Turner pointed out, the course of a life is understood in terms of time in the solar year (youth is springtime; old age is winter). Life is also conventionally conceptualized as a journey.

Gentner emphasized that in analogy, the key similarities lie in the relations that hold within the domains (e.g., the flow of electrons in an electrical circuit is analogically similar to the flow of people in a crowded subway tunnel), rather than in features of individual objects (e.g., electrons do not resemble people). Moreover, analogical similarities often depend on higher-order relations – relations between relations. For example, adding a resistor to a circuit causes a decrease in flow of electricity, just as adding a narrow gate in the subway tunnel would decrease the rate at which people pass through (where causes is a higher-order relation). In her structure-mapping theory, Gentner proposed that analogy entails finding a structural alignment, or mapping, between domains. In this theory, alignment between two representational structures is characterized by structural parallelism (consistent, oneto- one correspondences between mapped elements) and systematicity – an implicit preference for deep, interconnected systems of relations governed by higher-order relations, such as causal, mathematical, or functional relations.

Mapping is guided not only by relational structure and element similarity but also by the goals of the analogist. People draw analogies not to find a pristine isomorphism for its own sake but to make plausible inferences that will achieve their goals. Particularly when the mapping is inherently ambiguous, the constraint of pragmatic centrality – relevance to goals – is critical. Spellman and Holyoak investigated the impact of processing goals on the mappings generated for inherently ambiguous analogies.

The key idea of Holyoak and Thagard’s multiconstraint theory of analogy is that several different kinds of constraints – similarity, structure, and purpose – all interact to determine the optimal set of correspondences between source and target. A good analogy is one that appears coherent in the sense that multiple constraints converge on a solution that satisfies as many different constraints as possible. Everyday use of analogies depends on the human ability to find coherent mappings – even when source and target are complex and the mappings are ambiguous. For example, political debate often makes use of analogies between prior situations and some current controversy.

Analogical inference – using a source analog to form a new conjecture, whether it be a step toward solving a math problem, a scientific hypothesis, a diagnosis for puzzling medical symptoms, or a basis for deciding a legal case – is the fundamental purpose of analogical reasoning. Mapping serves to highlight correspondences between the source and target, including “alignable differences” – the distinct but corresponding elements of the two analogs. These correspondences provide the input to an inference engine that generates new target propositions. The basic form of analogical inference has been called “copy with substitution and generation”. CWSG involves constructing target analogs of unmapped source propositions by substituting the corresponding target element, if known, for each source element, and if no corresponding target element exists, postulating one as needed. This procedure gives rise to two important corollaries concerning inference errors. First, if critical elements are difficult to map (e.g., because of strong representational asymmetries such as those that hinder mapping a discrete set of elements to a continuous variable) then no inferences can be constructed. Second, if elements are mismapped, predictable inference errors will result.

It appears that when people notice the connection between a source and target, and they are sufficiently engaged in an effort to understand the target situation, analogical inferences will be generated by CWSG and then integrated with prior knowledge of the target. At least sometimes, an analogical inference becomes accepted as a stated fact. This result obviously has important implications for understanding analogical reasoning, such as its potential for use as a tool for persuasion.

In general, any kind of processing that helps people focus on the underlying causal structure of the analogs, thereby encouraging learning of more effective problem schemas, will improve subsequent transfer to new problems. For example, Gick and Holyoak found that induction of a “convergence” schema from two disparate analogs was facilitated when each story stated the underlying solution principle abstractly: “If you need a large force to accomplish some purpose, but are prevented from applying such a force directly, many smaller forces applied simultaneously from different directions may work just as well.” In some circumstances, transfer can also be improved by having the reasoner generate a problem analogous to an initial example.

When we think analogically, we do much more than just compare two analogs based on obvious similarities between their elements. Rather, analogical reasoning is a complex process of retrieving structured knowledge from long-term memory, representing and manipulating role-filler bindings in working memory, performing selfsupervised learning to form new inferences, and finding structured intersections between analogs to form new abstract schemas. The entire process is governed by the core constraints provided by isomorphism, similarity of elements, and the goals of the reasoner. These constraints apply in all components of analogical reasoning: retrieval, mapping, inference, and relational generalization. When analogs are retrieved from memory, the constraint of element similarity plays a large role, but relational structure is also important – especially when multiple source analogs similar to the target are competing to be selected. For mapping, structure is the most important constraint but requires adequate working memory resources; similarity and purpose also contribute. The success of analogical inference ultimately depends on whether the purpose of the analogy is achieved, but satisfying this constraint is intimately connected with the structural relations between the analogs. Finally, relational generalization occurs when schemas are formed from the source and target to capture those structural patterns in the analogs that are most relevant to the reasoner’s purpose in exploiting the analogy.

Deductive Reasoning, J. Evans

What exactly is deductive logic? As a model for human reasoning, it has one great strength but several serious weaknesses. The strength is that an argument deemed valid in logic guarantees that if the premises are true, then the conclusion will also be true. Consider a syllogism (an old form of logic devised by Aristotle) with the following form:

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

This is valid argument and will remain so no matter what terms we substitute for A, B, and C. For example,

All frogs are reptiles. No cats are reptiles. Therefore, no cats are frogs.

has two true premises and a true conclusion. Unfortunately, the argument is equally valid if we substitute terms as follows:

All frogs are mammals. No cats are mammals. Therefore, no cats are frogs.

A valid argument can allow a true conclusion to be drawn from false premises, as previously, which would make it seem a nonsense to most ordinary people (that is, not logicians). This is one weakness of logic in describing everyday reasoning, but there are others. The main limitation is that deductive reasoning does not allow you to learn anything new at all because all logical argument depends on assumptions or suppositions. At best, deduction may enable you to draw out conclusions that were only implicit in your beliefs, but it cannot add to those beliefs. There are also severe limitations in applying logic to real world arguments where premises are uncertain and conclusions may be made provisionally and later withdrawn.

The standard paradigm consists of giving people premises and asking them to draw conclusions. There are two key instructions that make this a deductive reasoning task. First, people must be told to assume the premises are true and (usually) are told to base their reasoning only on these premises. Second, they must only draw or endorse a conclusion that necessarily follows from the premises.

Modus Ponens (MP)
If p then q / p / Therefore q

Modus Tollens (MT)
If p then q / not-q / Therefore, not-p

For example, suppose we know that “if the switch is down then the light is on.” If I notice that the switch is down, then I can obviously deduce that the light is on (MP). If I see that the light is off, I can also validly infer that the switch is not down (MT). One of the difficulties with testing people’s logical ability with such arguments, however, is that they can easily imagine counterexample cases that block such valid inferences. For example, if the light bulb has burned out, neither MP not MT will deliver a true conclusion. That is why the instruction to assume the truth of the premises should be part of the deduction experiment. It also shows why deductive logic may have limited application in real world reasoning, where most rules – such as conditional statements – do have exceptions.

An argument is valid if there is no counterexample to it in which the premises hold and the conclusion does not. Although this accounts for deductive competence, the main finding on syllogistic reasoning is that people in fact endorse many fallacies. By analyzing the nature of the fallacies that people make and those they avoid, Evans et al. were able to provide strong evidence that people do not normally search for counterexample cases during syllogistic reasoning. Some fallacies are made as frequently as valid inferences and some as infrequently as on syllogisms where the conclusion is impossible. This strongly suggests that people consider only a single model of the premises, endorsing the fallacy if this model happens to include the conclusion.

People make many logical errors generally on deductive reasoning tasks. These errors are not necessarily random but often systematic, leading to description by term bias. We should note at this point that a bias is by definition a regular deviation from the logic norm and defer for the time being the question of whether biases should be taken to indicate irrationality.

One of the earliest known biases in conditional reasoning was that of “negative conclusion bias”, which affects several conditional inferences, including MT. Consider a subtly changed version of the earlier problem:

If the card does not have an A on the left, then it has a 3 on the right. The card does not have a 3 on the right. Therefore, the card has an A on the left.

The difference is that a negative has been introduced into the first part of the conditional and the conclusion is now affirmative.

Introducing negatives into conditional statements can also cause an effect known as matching bias. This is best illustrated in a problem known as theWason selection task. Although not strictly a deductive reasoning task, the selection task involves the logic of conditionals and is considered part of the literature on the deduction. In a typical abstract version of the problem, participants are shown four cards lying on a table and told that each has a capital letter on one side and a single figure number on the other. The visible sides are B L 2 9 They are told that the following rule applies to these four cards and may be true or false: If a card has a B on one side, then it has a 2 on the other side. The task is to decide which cards need to be turned over in order to check whether the rule is true or false. Wason argued that the correct choice is B and 9 because only a card with a B on one side and a number other than 2 on the other side could disprove the rule. Most subsequent researchers have accepted this normative analysis, although some argue against it on the assumption that people interpret the task as having to do with categories rather than specific cards. In any event, only around 10% of university students typically choose the B and 9. The most common choices are B and 2, or just B. Wason originally argued that this provided evidence of a confirmation bias in reasoning. That is, participants were trying to discover the confirming combination of B and 2 rather than the disconfirming combination of B and 9.

One of the most important biases investigated in the deductive reasoning literature is the belief bias effect, which is typically but inaccurately described as a tendency to endorse the validity of arguments when you agree with their conclusions.

People can only be judged to be in error relative to some normative system that may well be disputable. For example, philosophers have proposed alternative logics, and the standard propositional logic for deductive reasoning can be seen as mapping poorly to real world reasoning, which allows for uncertainty and the withdrawal of inferences in light of new evidence. The interpretation problem is that correctness of inference is judged on the assumption that the participant understands the task as the experimenter intended. This is also a pertinent criticism.

One way of dealing with the normative system problem is to distinguish between normative and personal rationality. Logical errors on deductive reasoning tasks violate normative rationality because the instructions require one to assume the premises and draw necessary conclusions. Whether they violate personal rationality is moot, however, because we may have little use for deductive reasoning in everyday life and carry over inappropriate but normally useful procedures instead. A different distinction is that between individual and evolutionary rationality. Stanovich argues that what serves the interests of the genes does not always serve the interests of the individual. In particular, the tendency to contextualize all problems against background belief and knowledge may prevent us from the kind of abstract reasoning that is needed in a modern technological society, so different from the world in which we evolved.

In logic, there is a distinction drawn between a valid inference and a sound inference. A valid inference may lead to a false conclusion, if at least one premise is false, as in the following syllogism: All students are lazy. No lazy people pass examinations. Therefore, no students pass examinations. The falsity of the previous conclusion is more immediately evident than that of either of the premises. However, the argument is valid, and so at least one premise must be false. A sound argument is a valid argument based on true premises and has the merit of guaranteeing a true conclusion. Because the standard deductive reasoning task includes instructions to assume the premises, as well as to draw necessary conclusions, psychologists generally assume they have requested their participants to make validity judgments. However, there is evidence that when familiar problem content is used, people respond as though they had been asked to judge soundness instead. This might well account for the suppression of MP. The inference is so obvious that it can hardly reflect a failure in reasoning.

People are also known to be influenced by the believability of the conclusion of the argument presented, reliably (and usually massively) preferring to endorse the validity of arguments with believable rather than unbelievable conclusions, the so-called “belief bias” effect. The standard experiment uses syllogisms and independently manipulates the believability of the conclusion and the validity of the argument. People accept both more valid arguments (logic effect) and more believable conclusions (belief effect), and the two factors normally interact.

System 1 (to use Stanovich’s terminology) is the ancient system that relies on associative learning through distributed neural networks and may also reflect the operation of innate modules. It is really a bundle of systems that most theorists regarded as implicit, meaning that only the final products of such a process register in consciousness, and they may stimulate actions without any conscious reflection. System 2, in contrast, is evolutionarily recent and arguably unique to humans. This system requires use of central working memory resources and is therefore slow and sequential in nature. System 2 function relates to general measures of cognitive ability such as IQ, whereas system 1 function does not. However, system 2 allows us to engage in abstract reasoning and hypothetical thinking. There is more recent supporting evidence of a neuropsychological nature for this theory. When resolving belief–logic conflicts in the belief bias paradigm, the response that dominates correlates with distinct areas of brain activity.

So where does the future of the deduction paradigm lie? I have suggested that we should use a much wider range of methods for studying human reasoning, especially when we are interested in investigating the pragmatic reasoning processes of system 1. In fact, there is no point at all in instructing people to make an effort at deduction unless we are interested in system 2 reasoning or want to set the two systems in conflict. However, this conflict is of both theoretical and practical interest and will undoubtedly continue to be studied using the deduction paradigm. It is important, however, that we understand that this is what we are doing. It is no longer appropriate to equate performance on deductive reasoning tasks with rationality or to assume that logic provides an appropriate normative account of everyday, real world reasoning.

Decision Making, R. LeBoeuf, E. Shafir

Although decisions can differ dramatically in scope and content, research has uncovered substantial and systematic regularities in how people make decisions and has led to the formulation of general psychological principles that characterize decision-making behavior. This chapter provides a selective review of those regularities and principles.

The classical treatment of decision making, known as the “rational theory of choice” or the “standard economic model,” posits that people have orderly preferences that obey a few simple and intuitive axioms. When faced with a choice problem, decision makers are assumed to gauge each alternative’s “subjective utility” and to choose the alternative with the highest. In the face of uncertainty about whether outcomes will obtain, decision makers are believed to calculate an option’s subjective expected utility, which is the sum of its subjective utilities over all possible outcomes weighted by these outcomes’ estimated probabilities of occurrence. Deciding then is simply a matter of choosing the option with the greatest expected utility; indeed, choice is believed to reveal a person’s subjective utility functions and, hence, his or her underlying preferences.

Although highly compelling in principle, the standard view has met with persistent critiques addressing its inadequacy as a description of how decisions are actually made. For example, Simon suggested replacing the rational model with a framework that accounted for a variety of human resource constraints, such as bounded attention and memory capacity, as well as limited time. According to this bounded rationality view, it was unreasonable to expect decision makers to exhaustively compute options’ expected utilities.

The mounting evidence has forced a clear division between normative and descriptive treatments. The rational model remains the normative standard against which decisions are often judged, both by experts and by novices. At the same time, substantial multidisciplinary research has made considerable progress in developing models of choice that are descriptively more faithful. Descriptive accounts as elegant and comprehensive as the normative model are not yet (and may never be) available, but research has uncovered robust principles that play a central role in the making of decisions. In what follows, we review some of these principles, and we consider the fundamental ways in which they conflict with normative expectations.

When facing a choice between a risky prospect that offers a 50% chance to win $200 (and a 50%chance to win nothing) versus an alternative of receiving $100 for sure, most people prefer the sure gain over the gamble, although the two prospects have the same expected value. Such preference for a sure outcome over a risky prospect of equal expected value is called risk aversion; people tend to be risk averse when choosing between prospects with positive outcomes.

However, when asked to choose between a prospect that offers a 50% chance to lose $200 (and a 50% chance of nothing) versus losing $100 for sure, most people prefer the risky gamble over the certain loss. This is because diminishing sensitivity applies to negative as well as to positive outcomes: The impact of an initial $100 loss is greater than that of an additional $100, which implies a convex value function for losses...Such preference for a risky prospect over a sure outcome of equal expected value is described as risk seeking.With the exception of prospects that involve very small probabilities, risk aversion is generally observed in choices involving gains, whereas risk seeking tends to hold in choices involving losses.

In addition, according to prospect theory, probabilities are not treated linearly; instead, people tend to overweight small probabilities and to underweight large ones. This, among other things, has implications for the attractiveness of gambling and of insurance.

Furthermore, research has suggested that the weighting of probabilities can be influenced by factors such as the decision maker’s feeling of competence in a domain, or by the level of affect engulfing the options under consideration. Such attitudes toward value and chance entail substantial sensitivity to contextual factors when making decisions.

The absence of uncertainty, however, does not eliminate preference malleability, and many of the principles discussed previously continue to exert an impact even on riskless decisions. Recall that outcomes can be framed as gains or as losses relative to a reference point, that losses typically “loom larger” than comparable gains, and that people tend to accept the presented frame. These factors, even in the absence of risk, can yield normatively problematic decision patterns.

A fundamental fact about the making of decisions is loss aversion: According to loss aversion, the pain associated with giving up a good is greater than the pleasure associated with obtaining it. This yields “endowment effects,” wherein the mere possession of a good (such that parting with it is rendered a loss) can lead to higher valuation of the good than if it were not in one’s possession.

Loss aversion thus promotes stability rather than change. It implies that people will not accept an even chance to win or lose $X, because the loss of $X is more aversive than the gain of$Xis attractive. In particular, it predicts a strong tendency to maintain the status quo because the disadvantages of departing from it loom larger than the advantages of its alternative.

The status quo bias can affect decisions in domains as disparate as job selection, investment allocation, and organ donation, and it can also hinder the negotiated resolution of disputes. If each disputant sees the opponent’s concessions as gains but its own concessions as losses, agreement will be hard to reach because each will perceive itself as relinquishing more than it stands to gain. Because loss aversion renders foregone gains more palatable than comparable losses, an insightful mediator may do best to set all sides’ reference points low, thus requiring compromises over outcomes that are mostly perceived as gains.

The tendency to adopt the provided frame can lead to “attribute-framing” effects. A package of ground beef, for example, can be described as 75% lean or else as 25% fat. Not surprisingly, it tends to be evaluated more favorably under the former description than the latter. Similarly, a community with a 3 .7% crime rate tends to be allocated greater police resources than one described as 96.3% “crime free”. Attribute-framing effects are not limited to riskless choice; for example, people are more favorably inclined toward a medical procedure when its chance of success, rather than failure, is highlighted. Attribute-framing manipulations affect the perceived quality of items by changing their descriptions. Part of the impact of such semantic factors may be due to spreading activation, wherein positive words (e.g., “crime-free”) activate associated positive concepts, and negative words activate negative concepts.

One way to avoid conflict in choice is to opt for what appears to be no choice at all, namely, the status quo...The addition of an attractive option increased conflict and diminished the number who ended up with either player, despite the fact that most preferred the initial alternative to the status quo. This violates what is known as the regularity condition, according to which the “market share” of an existing option – here, the status quo – cannot be increased by enlarging the offered set.

A related pattern was documented using tasting booths in an upscale grocery store, where shoppers were offered the opportunity to taste any of 6 jams in one condition, or any of 24 jams in the second. In the 6-jams condition, 40% of shoppers stopped to have a taste and, of those, 30% proceeded to purchase a jam. In the 24-jam condition, a full 60% stopped to taste, but only 3% purchased. Presumably, the conflict between so many attractive options proved hard to resolve. Further studies found that those choosing goods (e.g., chocolate) from a larger set later reported lower satisfaction with their selections than those choosing from a smaller set. Conflict among options thus appears to make people less happy about choosing, as well as less happy with their eventual choices.

The addition of some options can generate conflict and increase the tendency to refrain from choosing. Other options, however, can lower conflict and increase the likelihood of making a choice. Asymmetric dominance refers to the fact that in a choice between options A and B, a third option, A, can be added that is clearly inferior to A (but not to B), thereby increasing the choice likelihood of A. For example, a choice between $6 and an elegant pen presents some conflict for participants. However, when a less attractive pen is added to the choice set, the superior pen clearly dominates the inferior pen. This dominance provides a rationale for choosing the elegant alternative and leads to an increase in the percentage of those choosing the elegant pen over the cash. Along related lines, the compromise effect occurs when the addition of a third, extreme option makes a previously available option appear as a reasonable compromise, thus increasing its popularity.

Furthermore, a wealth of evidence suggests that people are not always aware of their reasons for acting and deciding. In one example, participants presented with four identical pairs of stockings and asked to select one showed a marked preference for the option on the right. However, despite this evidence that choice was governed by position, no participant mentioned position as the reason for the choice. Respondents easily generated “reasons” (in which they cited attributes, such as stocking texture), but the reasons they provided bore little resemblance to those that actually guided choice.

People tend to focus on the relative strengths of options (more compatible with choosing) when they choose, and on weaknesses (compatible with rejecting) when they reject. As a result, options’ positive features (the pros) loom larger in choice, whereas their negative features (the cons) are weighted relatively more during rejection. In one study, respondents were presented with pairs of options – an enriched option, with various positive and negative features, and an impoverished option, with no real positive or negative features. For example, consider two vacation destinations: one with a variety of positive and negative attributes, such as gorgeous beaches and great sunshine but cold water and strong winds, and another that is neutral in all respects. Some respondents were asked which destination they preferred; others decided which to forego. Because positive features are weighed more heavily in choice and negative features matter relatively more during rejection, the enriched destination was most frequently chosen and rejected. Overall, its choice and rejection rates summed to 115%, significantly more than the impoverished destination’s 85%, and more than the 100% expected if choice and rejection were complementary.

Decision contexts can facilitate or hamper attribute evaluation, and this can alter attribute weights. Not surprisingly, an attribute whose value is clear can have greater impact than an attribute whose value is vague. The effects of ease of evaluation, referred to as “evaluability,” occur, for example, when an attribute proves difficult to gauge in isolation but easier to evaluate in a comparative setting. In one study, subjects were presented with two second-hand music dictionaries: one with 20,000 entries but a slightly torn cover, and the other with 10,000 entries and an unblemished cover. Subjects had only a vague notion of how many entries to expect in a music dictionary; when they saw these one at a time, they were willing to pay more for the dictionary with the new cover than for the one with a cover that was slightly torn. When the dictionaries were evaluated concurrently, however, the number-of-entries attribute became salient: Most subjects obviously preferred the dictionary with more entries, despite the inferior cover.

Many of the inconsistency patterns described previously would not have arisen were decisions considered from a more global perspective. The framing of decisions, for instance, would be of little consequence were people to go beyond the provided frame to represent the decision outcomes in a canonical manner that is description independent. Instead, people tend to accept the decision problem as it is presented, largely because they may not have thought of other ways to look at the decision, and also because they may not expect their preferences to be susceptible to presumably incidental alterations.

Myopic decisions can occur when highly transient frames of mind are momentarily triggered, highlighting values and desires that may not reflect the decision maker’s more global preferences. Because choices often involve delayed consumption, failure to anticipate the labile nature of preferences may lead to the selection of later-disliked alternatives.

At the most basic level, transient mindsets arise when specific criteria are made momentarily salient. Grocery shopping while very hungry, for example, is likely to lead to purchases that would not have been made under normal circumstances. In a study of the susceptibility to temporary criterion salience, participants first received a “word perception test” in which either creativity, reliability, or a neutral topic was primed. Participants then completed an ostensibly unrelated “product impression task” that gauged their opinions of various cameras. Cameras advertised for their creative potential were rated as more attractive by those primed for creativity than by those exposed to words related to reliability or a neutral topic. Momentary priming thus impacted ensuing preferences, rendering more salient criteria that had not previously been considered important, despite the fact that product consumption was likely to occur long after such momentary criterion salience dissipated.

Emotions, or affect, also influence the associations or images that come to mind in decision making. Because images can be consulted quickly and effortlessly, an “affect heuristic” has been proposed with affective assessments sometimes guiding decisions. Furthermore, “anticipatory emotions” (e.g., emotional reactions to being in a risky situation) can influence the cognitive appraisal of decision situations and can affect choice just as drives and motivations can influence reasoning more generally. Emotion and affect thus influence people’s preferences; however, because these sentiments are often transient, such influence contributes to reversals of preference as momentary emotions and drives fluctuate. Inconsistency thus often arises because people do not realize that their preferences are being momentarily altered by situationally induced sentiments. Evidence suggests, however, that even when people are aware of being in the grip of a transient drive or emotion, they may not be able to “correct” adequately for that influence.

A review of the behavioral decision-making literature shows peoples’ preferences to be highly malleable and systematically affected by a host of factors not subsumed under the compelling and popular normative theory of choice. People’s preferences are heavily shaped, among other things, by particular perceptions of risk and value, by multiple influences on attribute weights, by the tendency to avoid decisional conflict and to rely on compelling reasons for choice, by salient identities and emotions, and by a general tendency to accept decision situations as they are described, rarely reframing them in alternative, let alone canonical, ways.

It is tempting to attribute many of the effects to shallow processing or to a failure to consider the decision seriously. After all, it seems plausible that participants who consider a problem more carefully might notice that it can be framed in alternate ways. This would allow a consideration of the problem from multiple perspectives and perhaps lead to a response unbiased by problem frame or other “inconsequential” factors. Evidence suggests, however, that the patterns documented previously cannot be attributed to laziness, inexperience, or lack of motivation. The same general effects are observed when participants are provided greater incentives, when they are asked to justify their choices, when they are experienced or expert decision makers, or when they are the types (e.g., “high need for cognition”) who naturally think more deeply about problems. These findings suggest that many of the attitudes triggered by specific choice problem frames are at least somewhat entrenched, with extra thought or effort only serving to render the dominant perspective more compelling, rather than highlighting the need for debiasing.

As it turns out, misprediction of experienced utility is common, in part because people misremember the hedonic qualities of past events, and in part because they fail to anticipate how enjoyment may be impacted by factors such as mere exposure, the dissipation of satiation, and the power of adaptation, even to dramatic life changes.

A Model of Heuristic Judgment, D. Kahneman, S. Frederick

The program of research now known as the heuristics and biases approach began with a study of the statistical intuitions of experts, who were found to be excessively confident in the replicability of results from small samples. The persistence of such systematic errors in the intuitions of experts implied that their intuitive judgments may be governed by fundamentally different processes than the slower, more deliberate computations they had been trained to execute. From its earliest days, the heuristics and biases program was guided by the idea that intuitive judgments occupy a position – perhaps corresponding to evolutionary history – between the automatic parallel operations of perception and the controlled serial operations of reasoning. Intuitive judgments were viewed as an extension of perception to judgment objects that are not currently present, including mental representations that are evoked by language. The mental representations on which intuitive judgments operate are similar to percepts. Indeed, the distinction between perception and judgment is often blurry: The perception of a stranger as menacing entails a prediction of future harm.

To represent intuitive and deliberate reasoning, we borrow the terms “system 1 ” and “system 2” from Stanovich and West. Although suggesting two autonomous homunculi, such a meaning is not intended. We use the term “system” only as a label for collections of cognitive processes that can be distinguished by their speed, their controllability, and the contents on which they operate. In the particular dual-process model we assume, system 1 quickly proposes intuitive answers to judgment problems as they arise, and system 2 monitors the quality of these proposals, which it may endorse, correct, or override. The judgments that are eventually expressed are called intuitive if they retain the hypothesized initial proposal with little modification.

We assume system 1 and system 2 can be active concurrently, that automatic and controlled cognitive operations compete for the control of overt responses, and that deliberate judgments are likely to remain anchored on initial impressions. We also assume that the contribution of the two systems in determining stated judgments depends on both task features and individual characteristics, including the time available for deliberation, mood, intelligence, cognitive impulsiveness, and exposure to statistical thinking.

The heuristics and biases research program has focused primarily on representativeness and availability – two versatile attributes that are automatically computed and can serve as candidate answers to many different questions. It has also focused principally on thinking under uncertainty. However, the restriction to particular heuristics and to a specific context is largely arbitrary. Kahneman and Frederick argued that this process of attribute substitution is a general feature of heuristic judgment; that whenever the aspect of the judgmental object that one intends to judge (the target attribute) is less readily assessed than a related property that yields a plausible answer (the heuristic attribute), individuals may unwittingly substitute the simpler assessment.

Whenever the heuristic attribute differs from the target attribute, the substitution of one for the other inevitably introduces systematic biases. In this treatment, we are mostly concerned with weighting biases, which arise when cues available to the judge are given either too much or too little weight. Criteria for determining optimal weights can be drawn from several sources.

The intent to judge a target attribute initiates a search for a reasonable value. Sometimes this search ends quickly because the required value can be read from a stored memory (e.g., the answer to the question “How tall are you?”) or a current experience (e.g., the answer to the question “How much do you like this cake?”). For other judgments, however, the target attribute does not readily come to mind, but the search for it evokes other attributes that are conceptually and associatively related. For example, a question about overall happiness may retrieve the answer to a related question about satisfaction with a particular aspect of life upon which one is currently reflecting.

Attribute substitution occurs when a relatively inaccessible target attribute is assessed by mapping a relatively accessible and related heuristic attribute onto the target scale. Some attributes are permanent candidates for the heuristic role because they are routinely evaluated as part of perception and comprehension and therefore always accessible. These natural assessments include physical properties such as size and distance and more abstract properties such as similarity, cognitive fluency in perception and memory, causal propensity, surprisingness, mood, and affective valence.

There is sometimes more than one candidate for the role of heuristic attribute. For an example that we borrow from Anderson, consider the question “Are more deaths caused by rattlesnakes or bees?” A respondent who has recently read about someone who died from a snakebite or bee sting may use the relative availability of instances of the two categories as a heuristic. If no instances come to mind, that person might consult his or her impressions of the “dangerousness” of the typical snake or bee, an application of representativeness. Indeed, it is possible that the question initiates both a search for instances and an assessment of dangerousness, and that a contest of accessibility determines the role of the two heuristics in the final response. As Anderson observed, it is not always possible to determine a priori which heuristic will govern the response to a particular problem.

Attribute substitution can be prevented by alerting respondents to the possibility that their judgment could be contaminated by an irrelevant variable. For example, although sunny or rainy weather typically affects reports of well-being, Schwarz and Clore found that weather has no effect if respondents are asked about the weather just before answering the wellbeing question. Apparently, this question reminds respondents that their current mood (a candidate heuristic attribute) is influenced by a factor (current weather) that is irrelevant to the requested target attribute (overall well-being). Schwarz also found that asking people to describe their satisfaction with some particular domain of life reduces the weight this domain receives in a subsequent judgment of overall well being. As these examples illustrate, although priming typically increases the weight of that variable on judgment (a system 1 effect), this does not occur if the prime is a sufficiently explicit reminder that brings the self-critical operations of system 2 into play.

The original goal of the heuristics and biases program was to understand intuitive judgment under uncertainty. Heuristics were described as a collection of disparate cognitive procedures, related only by their common function in a particular judgmental domain – choice under uncertainty. It now appears, however, that judgment heuristics are applied in a wide variety of domains and share a common process of attribute substitution, in which difficult judgments are made by substituting conceptually or semantically related assessments that are simpler and more readily accessible.

Our use of the dual-process terminology does not entail a belief that every mental operation (including each postulated heuristic) can be definitively assigned to one system or the other. The placement of dividing lines between “systems” is arbitrary because the bases by which we characterize mental operations (difficulty of acquisition, accessibility to introspection, and disruptability) are all continua. However, this does not make distinctions less meaningful; there is broad agreement that mental operations range from rapid, automatic, perception-like impressions to deliberate computations that apply explicit rules or external aids.

Motivated Thinking, D. Molden, E. Higgins

At one time or another, every one of us has engaged in “wishful thinking,” or “let our hearts influence our heads.” That is, every one of us has felt the effects of our motivations on our thought processes. Given this common everyday experience, it is not surprising that an essential part of early psychological research was the idea that drives, needs, desires, motives, and goals can profoundly influence judgment and reasoning. More surprising is that motivational variables play only a small role in current theories of reasoning. Why might this be?

The most prominent approach to motivated reasoning, in both classic and contemporary perspectives, has been to examine the influence on people’s thought processes of their needs, preferences, and goals to reach desired outcomes (or avoid undesired outcomes). Although the types of preferred outcomes that have been studied are highly diverse, they can be divided into two general classes: directional outcomes and nondirectional outcomes. Individuals who are motivated by directional outcomes are interested in reaching specific desired conclusions, such as impressions of themselves as intelligent, caring, and worthy people, or positive beliefs about others whom they find likeable or to whom they are especially close. In contrast, individuals who are motivated by nondirectional outcomes have more general concerns, such as reaching the most accurate conclusion possible) or making a clear and concise decision, whatever this conclusion or decision may be.

Whether outcome motivation is directional or nondirectional, however, this motivation has been conceptualized as affecting thought and reasoning in the same way: by directing people’s cognitive processes (e.g., their recall, information search, or attributions) in ways that help to ensure they reach their desired conclusions. That is, individuals’ preferences for certain outcomes are believed to often shape their thinking so as to all but guarantee that they find a way to believe, decide, and justify whatever they like.

Some of the first evidence for the effects on reasoning of motivations for positive selfevaluation grew out of work on attribution. Early attributional research found that when people were explaining their performance on tasks measuring important abilities they tended to take responsibility for their success (i.e., cite internal and stable causes, such as “I’m good at this task”) and to deny responsibility for their failure (i.e., cite external and unstable causes, such as “I was unlucky”). Such findings were typically described as stemming from desires for positive beliefs about the self.

One type of evidence for the role of motivation in self-serving attributions is that, independent of expectancies from prior success or failure, the more personally important a success is in any given situation, the stronger is the tendency to claim responsibility for this success but to deny responsibility for failure. Another type of evidence is that people’s attributions become increasingly self-serving when success or failure feedback is experienced as highly arousing.

In general, individuals tend to (1 ) give more credence to, and be more optimistic about, the validity of information that supports or confirms their standing as kind, competent, and healthy people; and (2) be more skeptical and cautious about information that threatens this standing.

Similar effects of people’s desire to view themselves positively have also been demonstrated in domains that do not directly involve health consequences. For instance, people who encounter scientific research that appears to support their cherished attitudes describe this research as being better conducted, and its conclusions as being more valid, than those who encounter the same research but believe it to be in conflict with their cherished attitudes. In addition, people have been shown to engage in considerable counterfactual thinking (i.e., mentally undoing the present state of affairs by imagining “if only . . .”) when evidence supporting predictions from a preferred theory or worldview fails to materialize. Such counterfactual thinking allows them to generate ways in which they were almost correct. However, when evidence is consistent with their theories, these same individuals do not engage in counterfactual thinking, which would force them to generate ways in which they were almost wrong.

Desires for positive self-evaluations also affect the quantity of people’s information processing. Specifically, such desires motivate decreased processing and quick acceptance of favorable evidence and increased processing and hesitant acceptance of unfavorable evidence. As one example, Ditto and colleagues demonstrated that, compared with evaluating favorable evidence, when people evaluate unfavorable evidence they spend a greater amount of time examining this evidence and spontaneously generate more alternate hypotheses about why it might be unreliable.

In addition to affecting the appraisal and encoding of new information, people’s desires for positive views of themselves (and certain well-liked others) have also been found to influence their use of stored knowledge in memory such as the selective activation of concepts and recall of events that support these views. These phenomena are exemplified in a series of studies by Santioso, Kunda, and Fong. Participants in these studies read fictitious articles revealing that either introverts or extroverts tend to have more academic and professional success. Following this, individuals who believed that introversionwas linked to success were more likely to recall, and were faster to recall, autobiographical instances of introverted behaviors than extroverted behaviors. The opposite pattern of resultswas found for individuals who believed that extroversion was linked to success.

In sum, motivations for directional outcomes can affect basic cognitive processes and influence thinking in several profound ways. These types of motivations affect not only how people search for, evaluate, and explain information in the world around them but also how they activate, access, and organize their knowledge about themselves and others. The next section reviews research indicating that motivations for nondirectional outcomes can be equally important.

Although less research exists concerning the cognitive effects of nondirectional outcome motivation, several varieties have been considered in some depth. Among these, the two most prominent are desires for accuracy and desires for clarity and conciseness, or closure. Here, we consider the effects of these two motivations (which, as will be discussed, often have opposing effects on information processing) on many of the same cognitive processes examined in the previous section.

In addition to self-serving biases that occur when people explain their own performance, as described previously, research on attribution has also identified more general biases. For example, there is the tendency for people to fixate on one particular cause for some action or event and then fail to adequately consider alternative causes that are also possible. Although these attributional biases have been largely considered from a purely cognitive standpoint, there is evidence to suggest that they can also be influenced by accuracy and closure motivations.

As discussed earlier, research on directional outcome motivation has demonstrated that people engage in increased evidence evaluations and prolonged information search when encountering evidence unfavorable to their preferred self-views and reduced evidence evaluation and information search when encountering evidence favorable to their preferred self-views. In contrast, accuracy motivation produces prolonged information search, and closure motivation produces reduced information search, regardless of the circumstances.

In addition to affecting the length of people’s analysis and evaluation of evidence, nondirectional outcome motivation can also influence the complexity of this analysis. Accuracy-motivated individuals form judgments that show greater consideration of conflicting opinions and evidence, whereas closure-motivated individuals form judgments that show less of this type of consideration. Tetlock and colleagues demonstrated these effects in experiments in which participants were asked to write down their thoughts about topics such as affirmative action, American foreign policy, and the causes of certain historical events. Responses were then coded for their integrative complexity, which was defined in terms of the degree to which multiple perspectives on an issue were both identified and then integrated into a framework that included complex connections between them. Findings with people who were both novices and experts on the issues they were analyzing (i.e., college students and professional historians, respectively) indicated that those with increased accuracy motivation provided a more integratively complex analysis, whereas those with increased closure motivation provided a less integratively complex analysis.

There is also evidence that people with high (versus low) accuracy motivation activate more pieces of individuating trait and behavioral information when forming impressions of others, whereas people with high (versus low) need for closure display an increased tendency to rely solely on categorical information during impression formation.

Overall, then, motivations for nondirectional outcomes can also affect basic cognitive processes and profoundly influence thinking. Whereas motivations for directional outcomes were earlier shown to alter how people activate, evaluate, and explain information during reasoning, motivations for nondirectional outcomes (at least in terms of the accuracy and closure motivations reviewed here) instead alter how much activation, evaluation, or explanation, in fact, occurs. Furthermore, as the findings presented here illustrate, such quantitative differences in thought can often affect the outcomes of people’s judgments and decisions just as much as the qualitative differences described previously.

Although there are often specific outcomes, such as positive self-views, that people have some preference for during judgment, most individuals still acknowledge there is some kind of “objective reality” about whatever information they are considering. That is, motivated thinking related to directional outcomes operates within whatKunda has called reality constraints. Therefore, although there is a degree to which people adjust their definitions of success, engage in selective recall, or seek to criticize unfavorable evidence, this does not make them entirely unresponsive to world around them, except perhaps in extreme circumstances.

Another important consideration of the effects of accuracy motivation on thinking and reasoning is that even when people high in accuracy motivation are free to engage in extended information processing this does not guarantee that they will arrive at more accurate judgments. One obvious example of this situation is finding that evidence beyond what is immediately and effortlessly available does not exist or has faded from memory. In an another manifestation, people are affected by certain biases outside their awareness or are aware of such biases but unaware of what the proper strategy is to correct them. In all these circumstances, although accuracy motivation might increase information search, recall, and consideration of multiple interpretations, it would not be expected to eliminate judgment errors, and might even increase them.

To summarize, both directional outcome motivations, where people have a specific preferred conclusion they are trying to reach, and nondirectional outcome motivations, where people’s preferred conclusions are more general, alter many basic cognitive processes during reasoning. These include (1 ) the explanation of events and behaviors; (2) the organization, recall, and activation of knowledge in memory; and (3 ) the pursuit and evaluation of evidence relevant to decision making. Outcome motivation effects involve both how such cognitive processes are initiated and directed as well as how thoroughly these processes are implemented. Moreover, in any given situation the specific cognitive processes influenced by outcome motivation are typically those that aid the gathering and interpretation of information supporting the favored outcome. In this self-fulfilling way, then, people’s outcome-motivated reasoning often successfully brings about their desired conclusions.

One alternate perspective that has more recently emerged and complements an outcome-based view proposes that people are motivated not only with respect to the outcomes of their judgments but also with respect to the manner in which they go about making these judgments. That is, not only do people have preferred conclusions, but they also have preferred strategies for reaching their conclusions. Therefore, independent of whatever outcome holds the most interest for them, people may be motivated to reach these outcomes using strategies that “feel right” in terms of, and allow them to sustain, their current motivational orientation.

Considering alternative hypotheses is a fundamental component of many varieties of thinking. How might eager versus vigilant strategic preferences influence this process? In general, an eager strategy of considering alternatives would involve attempting to attain hits and to ensure against errors of omission by generating and selecting any plausible hypotheses that could remotely be correct. However, a vigilant strategy of considering alternatives would involve attempting to make correct rejections and to ensure against errors of commission by generating and selecting only the most probable hypotheses that seem likely to be correct. Therefore people in a promotion focus would be expected to consider a greater number of alternatives during thinking and reasoning than people in a prevention focus.

Besides generating and evaluating hypotheses, anotherway in which people consider alternatives during reasoning is in their use of counterfactuals. As briefly mentioned, earlier counterfactual thinking involves mentally undoing the present state of affairs and imagining alternative realities “if only” different decisions had been made or actions been taken. Several different varieties of counterfactual thinking have been identified. One broad distinction that has been made is between thoughts that concern the reversal of a previous inaction (e.g., if only I had acted, things might have gone better), or additive counterfactuals, and thoughts that concern the reversal of a previous action (e.g., if only I hadn’t acted, things wouldn’t be so bad), or subtractive counterfactuals.

Because additive counterfactuals simulate the correction of a past error of omission, this type of thinking represents a more eager strategy of considering alternative realities. In contrast, because subtractive counterfactuals simulate the correction of a past error of commission, this type of thinking represents a more vigilant strategy of considering alternate realities. Therefore, a promotion focus should increase the generation of additive counterfactuals, and a prevention focus should increase the generation of subtractive counterfactuals.

Problem Solving, L. Novick, M. Bassok

According to Duncker, “A problem arises when a living creature has a goal but does not know how this goal is to be reached. Whenever one cannot go from the given situation to the desired situation simply by action [i.e., by the performance of obvious operations], then there has to be recourse to thinking”.

Given that a problem has been identified, the nature of people’s background knowledge pertaining to that problem has important implications for the solution-related thinking they do. To understand this thinking, it is important to distinguish (1 ) the solver’s representation of the problem (i.e., the solver’s understanding of the underlying nature of the problem) and (2) the sequence of steps the solver takes to get from the given situation to the goal.

A problem representation is a model of the problem constructed by the solver to summarize his or her understanding of the problem’s essential nature. Ideally, this model includes information about the goal, the objects and their interrelations, the operations that can be applied (i.e., the steps that can be taken) to solve the problem, and any constraints on the solution process.

For some problems, the primary work of solution is to find the best representation; for other problems, there is little uncertainty about the representation, and the primary work is to discover a solution path (or the best solution path) from the initial state of the problem (the situation as initially presented to the solver) to the goal state.

Regardless of the specific problem type, problem-solving behavior involves an inherent interaction between constructing a representation and generating a solution. However, some researchers are most interested in factors that affect the way solvers represent problems, whereas others look for regularities in the way solvers apply operators to get from the initial state to the goal state. Based on their main focus of interest, researchers devise or select problems that are likely to induce distinct representations (e.g., the trains and bird problem, problems of inducing structure) or to require repeated selection and application of operators within a particular problem representation (e.g., the Tower of Hanoi and other problems of transformation, problems of arrangement).

The Gestalt psychologists emphasized the importance of problem representation – how people view, interpret, or organize the given information – distinguishing the formation of a representation from the process of generating a solution. The Gestalt psychologists documented the impact of changes in perspective on problem difficulty as well as the effects of extraneous assumptions and prior knowledge on the way people understand problems and, therefore, generate problem solutions.

In contrast to the Gestalt psychologists, Newell and Simon emphasized the step-by-step process of searching for a solution path connecting the initial state to the goal state. Their research goal was to identify general-purpose strategies that humans use to solve a variety of problems. Newell and Simon and their colleagues were heavily influenced by the information-processing approach to cognitive psychology and by work in computer science on artificial intelligence. These influences led them to construct the General Problem Solver (GPS), a computer program that modeled human problem solving. A great strength of GPS was its ability to solve problems as different as the Tower of Hanoi problem and the construction of logic proofs with a single general-purpose strategy.

In the field of problem solving, researchers recognized that a fundamental weakness of GPS was its lack of domain knowledge. For every problem type, the generalpurpose strategy had to be supplemented with domain-specific knowledge. Moreover, research on expertise in knowledge-rich academic domains, such as mathematics, physics, and political science, especially during the late 1970s and early 1980s, made clear the necessity of taking domain knowledge into account for understanding problem solving. This research on expertise provided empirical evidence for assertions first made by Duncker decades earlier: In his discussion of expertise differences in the domain of mathematics, Duncker noted that “with ‘poor’ mathematicians, the thought-material is from the very beginning more thoroughly imbued with perceptual functions. For the ‘good’ mathematician, on the other hand, there remains a more abstract stratum . . . in which only the specific mathematical properties still exist”.

The step-by-step solution process is the sequence of actions solvers take to find and execute a procedure for generating a solution to the problem as they understand it. Researchers who study solution processes have made a distinction between algorithmic and heuristic strategies. An algorithm is a procedure that is guaranteed to yield the solution. One type of algorithm is a mathematical formula. For example, multiplying the length of the base of a rectangle times its height is guaranteed to yield the rectangle’s area.

Another type of algorithm – exhaustive search – involves checking every possible move. For example, one could solve the Tower of Hanoi problem by exhaustively considering every possible move in Figure 14.2. Similarly, one could solve a fourletter anagram by systematically evaluating the 24 possible permutations of the given letters (the solution is bird ). For problems with a large number of possible states, however, exhaustive search is impractical or impossible.

Clearly, some method is needed to prune the number of possible moves to be considered. Such pruning is necessary for human solvers owing to the limited capacity of working memory; it is also necessary for computers when, as in chess, the number of possible states is extremely large. Heuristics are problem-solving strategies that accomplish this goal. Although heuristics do not guarantee solution, they are highly likely to lead to success.

Newell and Simon's fundamental proposal was that problem solving could be conceptualized as a process of searching through a problem space for a path connecting the initial state of knowledge (the solver’s understanding of the given information) to the goal state (the desired solution). Problem space is the term Newell and Simon coined to refer to the solver’s representation of the task as presented. Briefly, a problem space consists of a set of knowledge states (the initial state, the goal state, and various possible intermediate states), a set of operators that allow movement from one knowledge state to another, and local information about the path one is taking through the space (e.g., the current knowledge state and how one got there).

Newell and Simon’s primary focus of investigation was the strategies solvers use to find a path connecting the initial state to the goal state. That is, they sought to discover regularities in how solvers search through a problem space. In a nutshell, search is a serial method for making incremental progress toward the goal by applying operators to move from one knowledge state to another adjacent knowledge state. Newell and Simon discovered that, for a wide variety of problems, solvers’ search is guided by a small number of heuristics.

Hill climbing is a heuristic in which, at each step, the solver applies the operator that yields a new state that appears to be most similar to the goal state. This heuristic can be used whenever solvers can define an evaluation function that yields information about the similarity of the problem state generated by a candidate operator to the goal state.

Means-ends analysis is a more sophisticated heuristic than hill climbing because it does not depend on simple similarity to the goal. This heuristic consists of the following steps: 1 . Identify a difference between the current state and the goal (or subgoal) state. 2. Find an operator that will remove (or reduce) the difference. 3 a. If the operator can be directly applied, do so, or 3 b. If the operator cannot be directly applied, set a subgoal to remove the obstacle that is preventing execution of the desired operator. 4. Repeat steps 1 to 3 until the problem is solved.

The key difference between hill climbing and mean-ends analysis is the online generation of subgoals in the latter heuristic. Adding new subgoals during problem solving greatly increases the power of heuristic search. Subgoals provide direction, and to the extent that they are appropriate, they can be expected to prune the space of possible states. Moreover, by assessing progress toward a required subgoal rather than the final goal, solvers may be able to make moves that otherwise seem unwise.

A large body of research has found that mean-ends analysis tends to be people’s preferred solution method for novel problems that are relatively free of specialized content and for which a definite goal is given.

Although people rely on general-purpose search heuristics when they encounter novel problems, because these heuristics are weak and fallible, they abort them as soon as they acquire some knowledge about the particular problem space. At that point, they switch to more specialized strategies. In general, whenever solvers have some relevant background knowledge, they tend to use stronger, albeit more narrowly applicable, domain-specific methods. The impact of learning and domain knowledge on strategy use led problem-solving researchers to turn their attention from the solution of knowledge-lean puzzles and riddles to problems that made connections to solvers’ background knowledge... As we noted in the introduction, background knowledge plays an important role in determining the representation a solver constructs for a problem, which, in turn, affects the processes the solver uses to generate a solution.

We stated informally at the outset that a problem representation is a model of the problem constructed by solvers to summarize their understanding of the problem’s essential nature. More specifically, a representation has four components: (1) a represented world – in this case, the description of the problem to be solved, (2) a representing world – the set of elements to be used to depict the objects and relations in the represented world, (3) a set of rules that map elements of the represented world to elements of the representing world, and (4) a process that uses the information in the representing world – in this case, to solve the problem. This last component highlights the link between representation and solution:Without some process that uses the information in the representation for some purpose, the so-called representation has no symbolic meaning (i.e., it does not serve a representational function).

The representation a solver uses to support and guide problem solving can be either internal (residing in working memory) or external (e.g., drawn on paper). In either case, the elements of the representing world may follow a variety of different formats. Some representations are best described as verbal or propositional or declarative. Others are pictorial or diagrammatic, such as a drawing of a pulley system, a matrix or network, and a bar or line graph. Finally, some representations are “runnable” mental models.

In general, solvers’ background knowledge affects whether and to what extent they focus their attention on problem aspects that are or are not relevant to determining the solution. In this section, we discuss three types of background knowledge that pertain to solvers’ understanding of the problem at hand. First, we consider solvers’ prior experience with a structurally similar or analogous problem. Second, we consider their generalized schemas for types of solution procedures as well as types of common representational tools (e.g., matrices). Third, we consider differences in problem representation that are due to differences in solvers’ domain expertise.

An example can be helpful for solving a novel problem only if the two problems have a similar underlying structure because a problem’s structure is what determines appropriate solution methods. The example will not be helpful if the problems only share a similar cover story and involve similar objects (e.g., a person, cookies, and boxes) but differ in their underlying structure (e.g., in the example Susan distributes cookies among boxes, but in the novel problem Leah removes one cookie from each box). Research on analogical problem solving (also referred to as analogical transfer) shows that solvers’ understanding, or representation, of a novel problem can be facilitated by prior experience with an analogous (i.e., structurally equivalent) problem. However, people may fail to retrieve an analogous problem from memory, or fail to apply an analogous solution, if they focus their attention on the solution-irrelevant differences between the example and the novel problem.

In addition to knowledge of specific problems encountered in the past, solvers also have in memory abstract schemas for types of problems, types of solution procedures, and types of representations. These schemas are abstract in the sense that they include information that is common to multiple problems of a particular type but exclude information that is idiosyncratic to the individual problems over which the abstraction has occurred. For example, an abstract schema for the convergence solution would specify that multiple, low-intensity forces converge from different directions on a central target, but it would not specify that the forces are soldiers (or rays) or that the target is a fortress (or a tumor). A number of studies have shown that schemas for solution procedures can be induced by comparing two or more analogous problems (with their solutions) or by successfully solving one problem by analogy to another (solved) problem, and such schema induction in turn facilitates understanding and solution of subsequent analogous problems.

Duncker was perhaps the first psychologist to note that experts and novices in a domain focus their attention on different aspects of that domain, leading them to construct problem representations that are quite different: Whereas experts’ representations tend to highlight solution-relevant structural features (in particular, meaningful causal relations among the objects in the problem), novices’ representations tend to highlight solution-irrelevant superficial features (e.g., the particular objects themselves or how the question is phrased). Evidence for these representational differences has been found using a wide variety of experimental tasks and procedures.

It is important to note that these representational differences between experts and novices (or between people who are highly skilled versus less skilled in a domain) are a matter of emphasis and degree. With increasing expertise/knowledge, there is a gradual change in the focus of attention and in the problems that are seen as related, and the extremes are not quite as extreme as summaries of the differences often suggest.

The Gestalt view is that insight problem solving is characterized by an initial work period during which no progress toward solution is made (i.e., an impasse), a sudden restructuring of one’s problem representation to a more suitable form, followed immediately by the sudden appearance of the solution. Thus, solving insight problems is all about representation with essentially no role for a step-by-step process of generating the solution. Although subsequent and contemporary researchers concur with the Gestalt view that getting the right representation is crucial, this view does not provide a complete understanding of the nature of insight solutions because the solution does not necessarily arise suddenly or fullblown following restructuring.

As discussed by Knoblich, Ohlsson, Haider, and Rhenius, theories of insight problem solving need to explain two phenomena concerning the interplay between representation and solution generation: (1 ) why solvers initially reach an impasse in solving a problem for which they have the necessary knowledge to generate the solution, and (2) what enables them to break out of the impasse. Two recent theories have attempted to account for these phenomena: progress monitoring theory, and Knoblich et al.’s representational change theory.

According to the progress monitoring theory, solvers use hill climbing in their solution attempts for insight as well as noninsight problems. Solvers are hypothesized to monitor their progress toward solution using a criterion generated from the problem’s current state. If solvers reach criterion failure, they seek alternative solutions by trying to relax one or more problem constraints.

According to Knoblich et al.’s representational change theory, insight problems are highly likely to evoke initial representations in which solvers place inappropriate constraints on their solution attempts. Impasses are resolved by revising one’s representation of the problem. According to Knoblich et al.’s theory, rerepresentation may happen through either of two mechanisms – constraint relaxation or chunk decomposition. Constraint relaxation involves deactivating some knowledge element that has constrained the operators being considered, thereby allowing application of new operators. Chunk decomposition involves breaking the bonds that link components of a meaningful unit in the problem.

Although it is possible to focus one’s research on one or the other of these components, a full understanding of problem solving requires an integration of the two, for the representation one constructs for a problem determines (or at least constrains) how one goes about trying to generate a solution.

By Duncker’s definition, humans engage in problem solving when they pursue the following goal-directed activities: (1 ) placing objects into categories and making inferences based on category membership, (2) making inductive inferences from multiple instances, (3 ) reasoning by analogy, (4) identifying the causes of events, (5 ) deducing logical implications of given information, (6) making legal judgments, and (7) diagnosing medical conditions from historical and laboratory data.

Complex Declarative Learning, M. Chi, S. Ohlsson

Complex learning takes longer than a few minutes and requires processes that are more complicated than the associative processes needed to memorize pairs of words. The materials that support complex learning – such as texts, illustrations, practice problems, and instructor feedback presented in classrooms and elsewhere – are often difficult to understand and might require extensive processing. For example, learning about the human circulatory system requires many component processes, such as integrating information from several sources, generating inferences, connecting new information with existing knowledge, retrieving appropriate analogies, producing explanations, coordinating different representations and perspectives, abandoning or rejecting prior concepts that are no longer useful, and so forth. Many of these component processes are still poorly understood so we have even less understanding of the complex process of learning a large body of knowledge.

Complex knowledge can be partitioned into two types: declarative knowledge and procedural knowledge. Declarative knowledge has traditionally been defined as knowledge of facts or knowing that, whereas procedural knowledge is knowing how. Declarative knowledge is descriptive and use independent. It embodies concepts, principles, ideas, schemas, and theories. Examples of declarative knowledge are the laws of the number system, Darwin’s theory of evolution, and the history of the Panama Canal. The sum total of a person’s declarative knowledge is his or her understanding of the way the world, or some part or aspect of the world, works, independently of the particular tasks the person undertakes.

Procedural knowledge, such as how to operate and troubleshoot a machine, how to solve a physics problem, or how to use a computer text editor, is prescriptive and use specific. It consists of associations between goals, situations, and actions. Research in cognitive neuroscience supports the reality of this distinction between declarative and procedural knowledge.

The most basic observation one can make about declarative knowledge is that humans have a lot of it. There are no precise estimates of the amount of knowledge a person possesses, but two attempts at an estimate seem well grounded. The first is an estimate of the size of the mental lexicon. The average college-educated adult knows between 40,000 and 60,000 words. The total number of words in the English language is larger than 100,000. Because concepts only constitute a subset of declarative knowledge, this represents a lower bound on the size of a person’s declarative knowledge base.

Knowledge does not grow as a set of isolated units but in some organized fashion. To capture the organization of the learners’ declarative knowledge, cognitive scientists operate with three distinct representational constructs: semantic networks, theories, and schemas. The key claim behind semantic networks is that a person’s declarative knowledge base can be thought of as a gigantic set of nodes (concepts) connected by links (relations). All knowledge is interrelated, and cognitive processes, such as retrieval and inferencing, operate by traversing the links. Early computer simulations of long-term memory for declarative knowledge explored variants of this network concept.

The semantic network idea claims that all knowledge is interrelated, but it does not propose any single, overarching structure for the network as a whole. Concepts and assertions are components of domains, but domains are not components of a yet higher level of organization. Domains relate to each other in a contingent rather than systematic way. Informal observations support this notion. We have one concept hierarchy for tools and another for furniture, but the node lamp appears in both. Home decorating is not a subset of cooking, or vice versa, but the two share the kitchen. The concept of tangled hierarchies describes one aspect of local, unsystematic contact points between internally structured domains.

Domains can also be represented as theories. Theories are “deep” representations in the sense of having well-articulated center-periphery structures. That is, a theory is organized around a small set of core concepts or principles – big ideas – on which the rest of the elements in the domain are dependent. The core knowledge elements are typically fundamental and abstract, whereas the peripheral ones are based on, derived from, or instances of the core ones. The most pristine examples of center-periphery structures are the formal axiomatic systems of mathematics and logic in which a small set of chosen axioms provide a basis for the proofs of all other theorems in a particular formal theory, and natural science theories, such as Newton’s theory of mechanical motion, Darwin’s theory of biological evolution, and the atomic theory of chemical reactions.

A well-developed center-periphery structure is often the hallmark of an expert’s representation of a domain, and a comparison between novices’ and experts’ representations of the same domain often reveals differences in the “depth” of their representations. However, one can raise the question of whether “depth” should also be construed as a characteristic of the domain itself. That is, are some domains intrinsically “deep” whereas others not, so that a centerperiphery structure is not an appropriate representation for some domains? If so, we would expect neither experts nor novices to construct “deep” representations of those domains.

The network concept codifies the intuition that everything is related to everything else, and the theory concept codifies the intuition that some knowledge elements are more important than others. The concept of a schema, however, codifies the intuition that much of our declarative knowledge represents recurring patterns in experience. Although the term “schema” has never been formally defined, the key strands in this construct are nevertheless clear. To a first approximation, a schema is a set of relations among a set of slots or attributes, where the slots can be thought of as variables that can take values within a specified range.

Schemas are bounded units of knowledge, and it is essential to their hypothesized function that they are retrieved or activated as units. That is, if one part of a schema (relation or slot) is activated, there is a high probability that the rest of the schema will also be retrieved. Schemas are typically abstract precisely because they represent recurring patterns in experience. Level of abstraction can vary.

Scripts are higher-order knowledge structures that represent people’s knowledge of informal or everyday events such as eating in a restaurant or visting the dentist’s office. Explanation patterns are schemas for how to construct explanations of particular types. Yet other schema-like constructs have been proposed. Chunks, explanation patterns, frames, plans, and scripts are variants of the basic idea that much declarative knowledge consists of representations of recurring patterns. For simplicity, we use the term schema throughout this chapter to refer to all these constructs.

In this chapter, we take the stance that networks, theories, and schemas are three partially overlapping but distinct theoretical constructs. Different aspects of the organization of declarative knowledge are best understood with the help of one or the other of these constructs, or with some mixture of the three. In summary, declarative knowledge bases are very large and they exhibit complex organization. The notion of semantic networks captures the fact that every part of a person’s knowledge is related, directly or indirectly, to every other part. Representations of particular domains vary in “depth,” that is, the extent to which they are characterized by a central set of fundamental ideas or principles to which other, more peripheral knowledge units are related. Declarative knowledge also represents recurring patterns in experience with schemas, small packets of abstract structural information that are retrieved as units and used to organize information. These three types of organization cannot easily be reduced to each other, and explanations of change in complex knowledge draw upon one or the other of these constructs or on some mixture of the three.

For adults, cumulative acquisition of individual pieces of knowledge – facts – must be pervasive and account for a large proportion of all learning. There is little mystery as to the processes of acquisition. People acquire them via perception and observation, via comprehension of oral and written discourse, and via inductive and deductive reasoning (i.e., by inferring new facts from prior knowledge, or by integrating new facts with old knowledge and making further inferences from the combination). A particularly interesting property of accretion is that it is self-strengthening. Many psychology studies have confirmed that what is encoded, comprehended, and inferred depends on the individual learner’s prior knowledge. In short, prior knowledge leads to more effective accretion, which in turn generates more prior knowledge.

We need to distinguish between two levels of learning. Comprehension as normally understood results in the construction of a specific instance of a schema or the accretion of schemarelevant facts. New information is assimilated to existing schemas. This is the basic mechanism of accretion. The size of the relevant declarative knowledge base increases without fundamental changes in structure. Deeper learning, however, results in some structural modification of the learner’s prior schema. The same distinction can easily be expressed within the other two theoretical frameworks that we use in this chapter. In network terms, accretion adds nodes and links without deleting or altering any prior ones, while deeper learning requires a reorganization of the network. In terms of intuitive theories, cumulative growth might develop the relations between the core principles and peripheral knowledge items, while deeper learning either develops the core principles or replaces or alters one or more of the core principles.

In network terms, connectedness can be defined as the density of relations between the knowledge elements. We would expect the density of connections in a representation to increase as the learner acquires more knowledge... In short, the better learned materials were more densely connected in an organized way, even though, overall, the two networks represented the same number of nodes and links.

The general point is that, as knowledge acquisition proceeds in a domain, the learner’s representation of that domain will increase in connectedness in a meaningful way.

The consistency of a knowledge representation refers to the degree to which the multiple assertions embedded in an intuitive theory can, in fact, be true at the same time. A person who claims that the Earth is round but who refuses to sail on the ocean for fear of falling over the edge is inconsistent in this sense.

It is reasonably certain that people prefer consistent over inconsistent beliefs, at least locally, and that the discovery of local inconsistency triggers cognitive processes that aim to restore consistency, just as Piaget, Festinger, Kuhn, and others have hypothesized.

However, the relation between experienced inconsistency and cognitive change is complex. Several investigators suggested that conflict triggers efforts to restore consistency only when the conflict is recognized by the learner him- or herself through reflection. When learners are alerted to inconsistencies and conflicts by an external source, they are more likely to either assimilate or dismiss them. Contradiction highlighted by an external source is likely to trigger change processes only if the learner is dissatisfied with his or her current conception. Furthermore, there are many ways to respond to inconsistency, and not all modes of response increase consistency (as opposed to bypassing the problem).

Consistency should also not be confused with level of expertise. A more knowledgeable person does not necessarily have a more consistent domain representation than someone who knows less. Ability to operate with inconsistency has often been proposed as a sign of intellectual sophistication, whereas insistence on total consistency has long been associated with dogmatism and lack of intellectual flexibility.

Reality is not simple, and almost any aspect of it can be described or represented at different levels of grain. As one learns more about something, one often comes to understand it at a finer grain. For example, learning how the human circulatory system works involves learning the components of the system, such as the heart, the lungs, blood, and blood vessels, and the relation that the contraction of the heart sends blood to different parts of the body.

Knowledge expansion via finer grain of representation is quite common in the sciences. The ultimate example is perhaps the reduction by chemists of material substances to molecules, described in terms of atoms, which in turn are re-represented by physicists in terms of elementary particles. We should keep in mind though that it is the experts’ representations of these domains that are refined, and novices’ representations do not necessarily follow suit.

It is not clear how often people are driven to expand their representations downward to a finer grain of analyses. In everyday life, people do not always feel the necessity to connect phenomena at one level to phenomena at more fine-grained levels. For example, people appear content to understand the weather at the level of wind, temperature, clouds, humidity, rain, and snow, without re-representing them at the finer levels of molecular phenomena available to the professional meteorologist.We do not yet understand the factors and processes that drive people to expand, but the possibility of such expansion is one important dimension of change in declarative knowledge.

A distinct type of change in the knowledge structure is needed when the learner’s current concepts are not sufficient to represent the phenomenon or system as a whole. The thing to be understood cannot be assimilated within any schema the learner has available. The learner can respond by creating a more complex schema. Although little is known about how more complex schemas are developed, one plausible hypothesis is that they are created by combining or assembling several existing schemas.

Changing the level of abstraction is closely related to, but different from, the process that we in normal parlance call change of perspective. A classic study by Anderson and Pichert demonstrates that this phrase does not merely refer to a metaphor but to a concrete psychological process. They gave subjects a text to read that described a home. They instructed subjects to take the perspective of either a burglar or a prospective home buyer. The results showed that the instructions led the subjects to remember different details, even when the perspective-taking instructions were given after the subjects had read the text.

Although we separate these seven dimensions analytically for purposes of this chapter, we do not suggest that a cognitive change typically moves along a single dimension. Most complex knowledge acquisition processes will involve simultaneous movement along more than one dimension. For example, learning about chemistry involves thinking of material substances as solids, liquids, and gases, instead of, for example, iron, water, and air; this is a move toward higher abstraction. At the same time, the chemistry student acquires a finer-grained analysis of material substances in terms of atoms and molecules and a large number of previously unknown isolated facts about such substances (e.g., their melting points). He or she might have to assemble a new schema such as dynamic equilibrium, which involves shifting the vantage point between the atomic level (where there are continuous processes) and the emergent macrolevel (where there is, nevertheless, stability). A year of high school chemistry is likely to require movement along all seven of these dimensions.We suggest that this is typical in the acquisition of complex declarative knowledge.

It is tempting to think of a novice as primarily lacking knowledge. The learning process is then naturally seen as a process of accretion – filling a void or adding information. Some of the types of changes described in the previous sections, such as increased connectedness and moves toward finer grain of representation, also have this cumulative nature because they significantly extend prior knowledge. However, several of the other types of changes, such as greater complexity, higher level of abstraction, and shifting vantage point, do not have this cumulative nature. Rather, they go further in that they re-represent the domain rather than merely add to it. However, in either the cumulative cases or the re-representation cases, the changes do not require that prior knowledge be rejected or replaced. For example, re-representing something at a higher level of abstraction does not require rejection of the prior representation because abstract and concrete representations of the same thing are not mutually incompatible. We can switch back and forth between conceptualizing something as a hammer and as a tool without any need to make a permanent choice between these two concepts. Thus, in these types of re-representation process, the old and the new representation can coexist, as well as the re-representing of two component concepts or schemas into a more complex concept or schema via assembly. The representations for the original concepts remain. In short, these types of cumulative and re-representational changes are monotonic.

As was mentioned earlier, in learning, new information is typically assimilated to existing schemas. Thus, one reason that misconceptions persist is that, when an instructor states the more veridical theory so it contradicts the learner’s prior misconceived knowledge, the new information is typically distorted in the process of being assimilated to the prior misconceived knowledge.

Distortion via assimilation is most plausible when the learner is unaware of the conflict between his or her prior knowledge and new information. However, even if the conflict between prior knowledge and new information is detected, it does not necessarily trigger productive change processes. Social psychologists and cognitive researchers have converged on very similar lists of potential modes of response to inconsistency. They agree that inconsistency often triggers evasive maneuvers that dismiss the inconsistency in some other way than by revising the relevant knowledge. The most basic mode of response is abeyance, that is, to postpone dealing with a contradiction on the grounds that not enough information is available to decide what, if anything, follows. One step removed from doing nothing is bolstering: The person who encounters information that contradicts some concept or belief X hastens to seek out supporting or confirming evidence that supports X. Festinger and others hypothesized that the need to reduce an inconsistency is proportional to the ratio of supporting to contradicting pieces of information. Thus, by drowning the contradicting piece of information in a flood of confirming ones, it is possible to lower the need to resolve the contradiction and hence to keep going without altering one’s knowledge. Another process with a similar outcome is recalibration, that is, to lower the importance one attaches to the conflicting thoughts, thus making the conflict itself less important and easier to ignore.

In summary, the mere presence of contradictory information is not sufficient to trigger productive cognitive change of the nonmonotonic kind. A conflict between prior knowledge and new information might go undetected, in which case the learner might blithely assimilate the new information to prior knowledge, probably distorting it in the process. Even if the learner detects the conflict, he or she might hold the new information in abeyance rather than respond to it. If he or she feels a need to deal with the contradiction, there is a repertoire of evasive maneuvers, including bolstering and recalibration of subjective importance, that will make the contradiction less disturbing without any revisions in prior knowledge. Finally, the productive learning processes discussed previously do not have the computational power to create a new conception that goes beyond the conceptual inputs to those processes. The prevalence of these three kinds of responses to encounters with contradictory information – distortion via assimilation, evading conflicts, and lacking computational power – raises the question of how an intuitive theory can ever be replaced. That is, how can a truly new theory or idea that is not an extension of old theories or ideas ever be acquired? Bereiter referred to this as the learning paradox.

One hypothetical path to a new theory is to edit or revise one’s existing theory piece by piece until the theory says something significantly different from what it said originally. We can conceptualize such a bootstrapping process as a series of local repairs of a knowledge structure. Local repairs require simple mechanisms such as adding links, deleting links, reattaching links, and so forth. The critical condition for local repairs is that the student recognize that the repairs are needed by reflecting on the differences between his or her existing knowledge and new knowledge. We have some evidence that the accumulation of local repairs can lead to a significant transformation of a person’s mental model of the circulatory system from a flawed single-loop model to the correct double-loop model.

Rokeach presented evidence from other than scientific domains that knowledge elements are more resistant to change the more central they are. It is plausible that transformation via bootstrapping a sequence of local repairs is less applicable the “deeper” the domain, at least as long as the change has to encompass the core principles to be complete. So perhaps this bootstrapping process cannot be considered a true nonmonotonic change mechanism.

If stepwise revisions can only go so far to explain nonmonotonic change, what alternative is there? Knowledge structures can be replaced. That is, an alternative representation of a domain is constructed in parallel with a prior one through processes that do not use the prior one as input. The old and the new representations then compete for the control of discourse and behavior in the course of question answering, explanation, reasoning, and problem solving. The new, presumably more veridical representation frequently wins, and the old one eventually fades from disuse.

Legal Reasoning, P. Ellsworth

Legal scholars have a tenacious intuition – or at least a strong hope – that legal reasoning is distinctive, that it is not the same as logic, or scientific reasoning, or ordinary decision making, and there have been dozens of attempts to describe what it is that sets it apart from these other forms of thinking. These attempts generate criticism, the critics devise new formulations that generate further criticism, and the process continues. In this chapter, I describe the primary forms of legal reasoning, the most important schools of thought about legal reasoning, and some of the major differences between legal reasoning and scientific reasoning.

When scholars write about “legal reasoning,” they are writing about judges. The lawyer does not have to decide the case, but only to make the strongest appeal for one side; lawyers’ reasoning is discussed in courses and writings on advocacy. Jurors interpret the evidence to decide what actually happened and apply the law given to them in the judge’s instructions to reach a verdict. The judge must also seek out the appropriate legal authority, deciding which laws and previous cases are applicable. Jurors are not supposed to reason about the law itself; that is the task of the judge. Judges are trained in the law, they know the statutes and precedents, and they have the experience of judging many cases and reading the decisions of other judges. Jurors do not provide reasons for their verdicts; judges often do. Finally, much of what is written about legal reasoning is about appellate court decisions, in which judges are primarily concerned with legal procedure and the law itself, not about who wins and loses, and in which they almost always must provide legal explanations for their decisions.

But that does not mean there are no commonly accepted characteristics of legal reasoning. There are. The problem that vexes legal scholars is that they are incomplete. Although they undoubtedly influence judicial reasoning, they are insufficient either to predict future outcomes or to provide a fully satisfactory account for past ones. The two most common reasoning strategies, taught in every law school course on legal reasoning and writing, are the deductive method (rule-based reasoning) and the analogical method (case-based reasoning). These strategies are not unique to legal reasoning. They are commonly described in relation to scientific reasoning as well. What is distinctive about these forms of reasoning in the legal context is not so much the process but the context, the raw materials to which the processes are applied, and the nature of the rules.

In deductive scientific reasoning, there is a general law or theory, and the scientist uses that theory to infer what will happen in some particular fact situation, makes a prediction, and designs an experiment to test it. If the prediction is not confirmed, there are three possibilities: The deduction was flawed, the experiment was flawed, or the theory is flawed. In deductive legal reasoning, the decision maker begins with a specific set of facts, looks at the law that applies to those facts, and reaches a verdict.

In practice, there are many ways in which ambiguity can creep into this apparently clear logical process. First, the decision maker is faced with a specific set of facts. If he or she is a judge, there are almost always two versions of the facts. It is the attorneys’ job to organize the facts in a way that fits the legal outcome they wish to achieve, and they do this by emphasizing different facts and, often, different legal precedents. “[T]he law determines which facts are relevant while at the same time, the facts determine which lawis relevant”. There may be more than one law that is potentially applicable. There may be several statutory provisions that might be relevant, and the two opposing counsel may argue that a different rule is the one that should control this case. The statute itself may violate a higher rule, such as the state or federal constitution. The rule may be ambiguous, as in a ban on “excessive noise,” or the application of the “reasonable person” standard (“Would a reasonable person have believed that her life was in danger?”).

In the Anglo-American common law tradition,1 cases are decided by examining the patterns of decisions in earlier, related cases. No case has meaning in isolation, and general rules and propositions are useless without “the heaping up of concrete instances”, except in very simple cases.

Lawyers have a certain leeway in their selection of which facts to emphasize, in their interpretation of the facts, and in their description of the legal significance of those facts. Like the scientist, the lawyer may identify some principle that explains why the current case should be considered an example of the first group rather than the second. The judge examines the strengths and weaknesses of the arguments of the two parties and either chooses between them or develops a different principle for placing the present case in the context of the past ones.

When legal educators claim that the basic mission of the first year of law school is to train the student to “think like a lawyer,” it is this sort of analogical reasoning they generally have in mind – the ability to spot the factual and legal similarities and (more important) differences between the case under study and related previous cases and to recognize which similarities and differences are relevant (e.g., the defendant’s state of mind) and which are not (e.g., the defendant’s name). This entails defining the universe of possibly applicable cases and deciding which ones match the current case most closely and which, although apparently similar, do not apply.

The essence of legal formalism is the idea that “a few basic top-level categories and principles formed a conceptually ordered system above a large number of bottom-level rules. The rules themselves were, ideally, the holdings of established precedents, which upon analysis could be seen to be discovered from the principles”. In other words, there is a pyramid of rules with a very few fundamental “first principles” at the top, from which mid-level and finally a large number of specific rules could be derived. The legal decision maker, faced with a case to be decided, would study the body of law and discover the rule that determined the correct result.

There were critics of legal formalism from the very beginning. The alternative view is illustrated in two famous remarks by Oliver Wendell Homes, Jr.: “The life of the law has not been logic: It has been experience”, and “general principles do not decide concrete cases” (dissenting opinion in Lochner v. New York, 1905). Holmes and, later, critics such as Pound, Llewellyn, and Cardozo argued that legal principles were not “discovered” by careful research into the rules and principles, and that such research, however diligent, would not yield definite and incontrovertible answers in any but the easiest cases. Instead of clear distinctions between the cases decided in one way and those decided in the other (for the plaintiff or the defendant in a medical malpractice case, for example), there is overlap and fuzziness at the boundary and, in the end, the judge creates the defining distinction rather than discovering it. The distinctions were often arbitrary, not logical, and influenced by the judge’s own sense of what the right outcome should be. The fundamental principles and legal rules were important and provided considerable guidance to the judge but, in most cases, they were insufficient to determine the outcome. The certainty and sense of inevitability expressed in judicial opinions was quite unjustified. As time goes by and the legal landscape becomes dense with more and more intermediate cases, the failures of formalism become increasingly apparent.

The tenets of legal formalism still exercise a strong influence on the way judicial opinions are written. Decisions typically are presented as the inevitable consequence of a careful analysis of the facts and the applicable law based on the classification of this case in relation to previous cases. The correct decision and the governing principles are described as discovered, not created, by the judge, and are expressed with great certainty, as though there were no room for doubt.

Legal realism arose in opposition to formalism and can be seen as an extension and elaboration of Holmes’s early skepticism. Legal realists rejected the formalist ideas that the law was a self-contained logical system providing for the scientific, deductive derivation of the right answer in all new cases. They regarded this view as a vain daydream disconnected from the real world influences on legal decision makers – hence the label “legal realism.” In a strict formalist analysis, two different judges should always judge the same case in the same way unless one of them was mistaken in his3 understanding of the facts or the law. Clearly this was not the case. In the nineteenth century, as now, courts were often divided. There were judges in the majority and there were dissenters, and no one seriously argued that the dissenters were incompetent or in need of retraining. Of course the formalists did not believe this was the way the world really worked, but they did believe that the legal system could approximate that ideal and that it was an ideal worth striving for. The legal realists believed that itwas an impossible ideal and that it was a waste of time to strive for it. According to the legal realists, instead of reflecting an abstract set of nearly immutable principles, the law reflects historical, social, cultural, political, economic, and psychological forces, and the behavior of individual legal decision makers is a product of these forces. It therefore is not surprising that different judges, with different goals and backgrounds, should decide cases differently, and contrary decisions do not imply that some judges must be “wrong.”

“Jurisprudence,” Roscoe Pound argued, “is the last in the march of sciences away from the method of deduction from predetermined conceptions”. The strict doctrinal approach blinded legal writers to two essential considerations: first, the purposes of the law – the goal of doing justice rather than following the letter of the law; and second, the social, cultural, and psychological factors that influenced behavior, including the behavior of lawmakers and judges. Blind adherence to the abstract law-on-the-books might make for greater certainty and predictability, but “reasonable and just solutions of individual cases” were “too often sacrificed”.

Pound argued that legal scholarship and judicial decisions should “take more account, and more intelligent account, of the social facts upon which law must proceed and to which it is to be applied”. The focus should not be on the abstract content of the laws but on how they actually work. It is important to consider the purpose of laws and to modify them if these purposes are not being achieved. And judges should regard the law as suggestive rather than determinative of their decisions: If strict application of the law would result in an outcome that is unjust or contrary to the purpose of the law, then flexibility in the cause of justice is appropriate.

Karl Llewellyn, one of the most important figures in the group, argued that law was about “disputes to be settled and disputes to be prevented”, not about rules; about what legal decision makers do, not what they say. Legal rules were regarded as, at best, post hoc justifications and, at worst, criteria that could lead judges to unjust decisions. Advocates in a trial could usually describe the facts and the law so as to produce coherent, complete, persuasive arguments for two diametrically opposite conclusions.

The agenda of the legal realists was both descriptive and prescriptive. According to Felix Cohen, “Fundamentally, there are only two significant questions in the field of law. One is, ‘How do courts actually decide cases of a given kind?’ The other is, ‘How ought they to decide cases of a given kind?’”. The answer to the descriptive question was that courts do not decide cases on the basis of laws because the law always allows for multiple answers. In considering what sort of forces do influence case outcomes, different scholars emphasized social and cultural forces, unconscious psychological drives, or just a process of intuition that eventually culminated in a Gestalt-like “Aha effect” after long rumination. These influences affect the assessment of the actual facts of the case – the credibility of the witnesses, the plausibility of the stories, as well as the judge’s “sense of how the law ought to respond to these facts”.

The intellectual enterprise of legal scholarship, therefore, should be to describe the actual behavior of courts, taking account of the broader social context. The realists were confident that this behavior would not be predictable from written legal doctrine or statutes. Instead, the legal rules and concepts would turn out to be consequences, rather than causes, of judges’ behavior. To understand how judges reach their decisions, it is important to analyze their social backgrounds, previous experience, and role demands and the general political, social, and economic pressures of the times.

The description of what courts actually do was supposed to explore not only the causes of judicial decisions but also their consequences.Astudy of consequences is essential to answer the second question, “How ought [courts] to decide cases of a particular kind?” Judicial decisions affect human behavior, often favoring one group’s interests over another, and they affect future judicial decisions. Careful study of these consequences would allow for better-informed judicial decisions and better laws.

Prescriptively, the realists argued first that in applying the law, judges ought to consider the purpose of the law and, second, that they should focus on the particulars of the case and compare it with the particulars of preceding cases, rather than looking for broad general principles. Consideration of the purposes of the law was supposed to enhance the fairness and the consistency of decisions, and blind application to the rule without considering its purpose would lead to bad decisions. To facilitate this approach, legislators and judges should make the reasons for the law explicit; to provide appropriate guidance to future judges: “Only the rule which shows its reason on its face has ground to claim maximum chance of continuing effectiveness”. Because social conditions were constantly changing, however, judges should be free to revise and reject even rules with clearly stated purposes; the development of law, like the development of science, should be a never-ending process of examination and re-examination.

Some of the realists believed that close examination of the prior body of cases required more than a reading of the cases alone. Some felt that an education in social science was necessary to fully understand the social forces influencing the parties and the judge. Others felt that legal researchers should create databases on the background of judges and their decisions, the frequency with which laws on the books were actually enforced, whether they are enforced against some groups more than others, whether patterns of enforcement have changed over time (e.g., obscenity laws), and so on.

According to Duncan Kennedy, “Legal argument is the process of creating the field of law through restatement rather than rule application”. The thought process evolves in time, beginning as a conflict and ending as certainty. Once a strategy is chosen, the judge no longer can imagine any compelling counterargument. Simon recently updated this analysis in the light of more recent research in social and cognitive psychology and showed that it has considerable power even in cases in which the judge has no particular political motivation: An incoherent mass of contradictions develops into a coherent decision in which no opposing argument carries any weight, but all turn out upon close examination to support the decision.

Nonetheless, the judge and the scientist have different tools available to them, different constraints, and different goals. Science demands no final decisions; it is an ongoing process. If the evidence is murky, scientists can wait, can reserve judgment until they can conduct further research. And they can figure out what further research needs to be done to answer the question, and do it. Judges can neither reserve judgment nor go beyond the data presented in court, however ambiguous those data might be. They cannot carry out further research, nor wait until others have done so; they must decide.

In legal reasoning, there is no empirical option. Judges must work with the information given to them, and that information consists entirely of what other people have said and the judge’s own knowledge. Judges listen to testimony and arguments and read the law, scholarly works, and the opinions of other judges; they arrange and rearrange these elements, selecting, interpreting, and looking for a rule that “holds good for the matter at hand”. The conclusion that the judge finally reaches is not empirically tested and cannot be disconfirmed.

If two scientists make opposite predictions, someone will do a study to try to choose between them or otherwise clarify the question. If a judge makes a decision, it is final unless it is appealed. If it is appealed, the appellate court rarely re-examines the facts and certainly does not invite new evidence but decides whether the lower court made a legal (procedural) error. The final decision is the decision of the majority, and a five to four decision in the Supreme Court has the same precedential authority as a unanimous decision. When the Court is split four to four, the views of the ninth, “swing” Justice decide the case and can have precedential force – even if those views are quite idiosyncratic.

The need to decide the particular case one way or the other also pushes legal reasoning toward categorical thinking: A person is either sane (guilty) or insane (not guilty); an unfit parent (someone else gets the child) or fit (he or she may get the child); a future danger to society (execution permitted) or not (execution not permitted, barring other aggravating factors). Psychologists consider sanity, fitness, and dangerousness to be continuous variables with no great gulf between the sane and the insane, the fit and the unfit, the safe and the dangerous, and many intermediate cases. But a legal case has to be decided for one party or the other, and so variables that are continuous are forced to become dichotomous. Sometimes there are more than two categories (first-degree murder, second-degree murder, and manslaughter), but a line must always be drawn.

This concern with certainty and the need to make dichotomous judgments may help explain why judges and legal scholars are often uncomfortable with probabilistic statements and probabilistic data. Scientists regularly make explicit quantified probability judgments; lawyers and judges do not – certainly not about the ultimate issues. For example, they strongly resist placing a numerical value on the “reasonable doubt” standard: Is it 95% certainty, 99% certainty? Jurors are generally just given the stock phrase, sometimes supplemented by other phrases, such as “to a moral certainty” or “firmly convinced.”

The law sees behavior as caused by people’s beliefs, desires, and preferences. Ideas of free choice and free will are still fundamental to legal thinking and largely unquestioned. This emphasis creates another source of tension between law and the social sciences because social science takes a much more deterministic point of view, emphasizing cultural, sociological, psychological, biological, and, especially in psychology, situational forces on behavior. The fact that economics is the social science that has been most successful in law schools is not surprising given this model; of all the social sciences, economics is the one most wedded to a free choice theory of behavior.

Legal reasoning is a form of expert reasoning. Einstein argued that expert reasoning – in particular, scientific reasoning – is “nothing but a refinement of our everyday thinking”. Like everyday problem solving and scientific reasoning, legal reasoning begins by examining a set of facts and figuring out what happened and why. Of course, some of the “facts” may be fictions, and the judge must decide which to believe and which to reject, but that is true of all natural problem solving. Information is selected and rejected as part of the process of creating a coherent story.

Scientific Thinking and Reasoning, K. Dunbar, J. Fugelsang

Scientific thinking refers to the mental processes used when reasoning about the content of science (e.g., force in physics), engaged in typical scientific activities (e.g., designing experiments), or specific types of reasoning that are frequently used in science (e.g., deducing that there is a planet beyond Pluto). Scientific thinking involves many general-purpose cognitive operations that human beings apply in nonscientific domains such as induction, deduction, analogy, problem solving, and causal reasoning.

What distinguishes research on scientific thinking from general research on cognition is that research on scientific thinking typically involves investigating thinking that has scientific content. A number of overlapping research traditions have been used to investigate scientific thinking.We cover the history of research on scientific thinking and the different approaches that have been used, highlighting common themes that have emerged over the past fifty years of research.

The thought processes underlying scientific thinking have fascinated both scientists and nonscientists because the products of science have transformed our world and because the process of discovery is shrouded in mystery. Scientists talk of the chance discovery, the flash of insight, the years of perspiration, and the voyage of discovery. These images of science have helped make the mental processes underlying the discovery process intriguing to cognitive scientists as they attempt to uncover what really goes on inside the scientific mind and how scientists really think. Furthermore, the questions, “Can scientists be taught to think better, avoiding mistakes of scientific thinking?” and “Could the scientific process be automated such that scientists are no longer necessary?” make scientific thinking a topic of enduring interest.

Bacon’s Novumm Organum, in 1620, sketched out some of the key features of the ways that experiments are designed and data interpreted. Over the ensuing 400 years, philosophers and scientists vigorously debated the appropriate methods that scientists should use. These debates over the appropriate methods for science typically resulted in the espousal of a particular type of reasoning method such as induction or deduction. It was not until the Gestalt psychologists began working on the nature of human problem solving during the 1940s that experimental psychologists began to investigate the cognitive processes underlying scientific thinking and reasoning.

Jerome Bruner and his colleagues at Harvard argued that a key activity in which scientists engage is to determine whether or not a particular instance is a member of a category. For example, a scientist might want to discover which substances undergo fission when bombarded by neutrons and which substances do not. Here, scientists have to discover the attributes that make a substance undergo fission. Bruner et al. saw scientific thinking as the testing of hypotheses and collecting of data with the end goal of determining whether something is a member of a category or not. They invented a paradigm in which people were required to formulate hypotheses and collect data that test their hypotheses. Using this approach, Bruner et al. identified a number of strategies people use to formulate and test hypotheses. They found that a key factor determining which hypothesis testing strategy people use is the amount of memory capacity the strategy takes up. Another key factor they discoveredwas that it is much more difficult for people to discover negative concepts (e.g., not blue) than positive concepts (e.g., blue). Although the Bruner et al. research is most commonly thought of as work on concepts, they saw their work as uncovering a key component of scientific thinking.

Whereas Bruner et al. focused on the different types of strategies people use to formulate hypotheses, Wason focused on whether people adopt a strategy of trying to confirm or disconfirm their hypotheses... Wason concluded that people try and confirm their hypotheses, whereas normatively speaking, they should try and disconfirm their hypotheses. One implication of this research is that confirmation bias is not just restricted to scientists but is a general human tendency.

Allan Newell, proposed that scientific thinking is a form of problem solving. He proposed that problem solving is a search in a problem space... Simon, colleague of Newell, devoted considerable time to understanding many different scientific discoveries and scientific reasoning processes. The common thread in his research was that scientific thinking and discovery is not a mysterious magical process but a process of problem solving in which clear heuristics are used. Simon’s goal was to articulate the heuristics that scientists use in their research at a fine-grained level. He built many programs that simulated the process of scientific discovery and articulated the specific computations that scientists use in their research. Particularly important was Simon and Lea’s work demonstrating that concept formation and induction consist of a search in two problem spaces: a space of instances and a space of rules. This idea has been highly influential on problem-solving accounts of scientific thinking.

Simon argued that both scientific thinking in general and problem solving in particular could be thought of as a search in a problem space. A problem space consists of all the possible states of a problem and all the operations that a problem solver can use to get from one state to the next. According to this view, by characterizing the types of representations and procedures people use to get from one state to another, it is possible to understand scientific thinking. Scientific thinking therefore can be characterized as a search in various problem spaces.

Klahr and Dunbar extended the search in a problem space approach and proposed that scientific thinking can be thought of as a search through two related spaces – an hypothesis space and an experiment space. Each problem space that a scientist uses will have its own types of representations and operators used to change the representations. Search in the hypothesis space constrains search in the experiment space. Klahr and Dunbar found that some participants move from the hypothesis space to the experiment space, whereas others move from the experiment space to the hypothesis space. These different types of searches lead to the proposal of different types of hypotheses and experiments. More recent work has extended the dual-space approach to include alternative problem-solving spaces, including those for data, instrumentation, and domain-specific knowledge.

Many researchers have regarded testing specific hypotheses predicted by theories as one of the key attributes of scientific thinking. Hypothesis testing is the process of evaluating a proposition by collecting evidence regarding its truth. Experimental cognitive research on scientific thinking that specifically examines this issue has tended to fall into two broad classes of investigations. The first class is concerned with the types of reasoning that lead scientists astray, blocking scientific ingenuity. A large amount of research has been conducted on the potentially faulty reasoning strategies that both participants in experiments and scientists use such as considering only one favored hypothesis at a time and how this prevents scientists from making discoveries. The second class is concerned with uncovering the mental processes underlying the generation of new scientific hypotheses and concepts. This research has tended to focus on the use of analogy and imagery in science as well as the use of specific types of problem-solving heuristics.

Turning first to investigations of what diminishes scientific creativity, philosophers, historians, and experimental psychologists have devoted a considerable amount of research to “confirmation bias.” This occurs when scientists consider only one hypothesis (typically the favored hypothesis) and ignore alternative hypotheses or other potentially relevant hypotheses. This important phenomenon can distort the design of experiments, formulation of theories, and interpretation of data. Beginning with the work of Wason and as discussed previously, researchers have repeatedly shown that when participants are asked to design an experiment to test a hypothesis, they predominantly design experiments they think will yield results consistent with the hypothesis. Using the 2-4-6 task mentioned earlier, Klayman and Ha showed that in situations in which one’s hypothesis is likely to be confirmed, seeking confirmation is a normatively incorrect strategy, whereas when the probability of confirming one’s hypothesis is low, then attempting to confirm ones hypothesis can be an appropriate strategy.

Confirmation bias is very difficult to overcome. Even when participants are asked to consider alternate hypotheses, they often fail to conduct experiments that could potentially disconfirm their hypothesis. Tweney and his colleagues provide an excellent overview of this phenomenon in their classic monograph “On Scientific Thinking”. The precise reasons for this type of block are still widely debated. Researchers such as Michael Doherty have argued that limitations in working memory make it difficult for people to consider more than one hypothesis. Consistent with this view, Dunbar and Sussman showed that when participants are asked to hold irrelevant items in working memory while testing hypotheses, participants are unable to switch hypotheses in the face of inconsistent evidence. Although limitations of working memory are involved in the phenomenon of confirmation bias, even groups of scientists can display confirmation bias.

Much of scientific thinking and scientific theory building pertains to the development of causal models between variables of interest. For example, does smoking cause cancer, Prozac relieve depression, or aerosol spray deplete the ozone layer? Scientists and nonscientists alike are constantly bombarded with statements regarding the causal relationship between such variables. How does one evaluate the status of such claims? What kinds of data are informative? How do scientists and nonscientists deal with data that are inconsistent with their theory?

One important issue in the causal reasoning literature that is directly relevant to scientific thinking is the extent to which scientists and nonscientists are governed by the search for causal mechanisms (i.e., the chain of events that lead from a cause to an effect) versus the search for statistical data (i.e., how often variables co-occur). This dichotomy can be boiled down to the search for qualitative versus quantitative information about the paradigm the scientist is investigating. Researchers from a number of cognitive psychology laboratories have found that people prefer to gather more information about an underlying mechanism than covariation between a cause and an effect. That is, the predominant strategy that students in scientific thinking simulations use is to gather as much information as possible about how the objects under investigation work rather than collecting large amounts of quantitative data to determine whether the observations hold across multiple samples. These findings suggest that a central component of scientific thinking may be to formulate explicit mechanistic causal models of scientific events.

One of the most basic characteristics of science is that scientists assume that the universe that we live in follows predictable rules. Very few scientists in this century would refute the claim that the earth rotates around the sun, for example. Scientists reason from these rules using a variety of different strategies to make new scientific discoveries. Two frequently used types of reasoning strategies are inductive and deductive reasoning. In the case of inductive reasoning, a scientist may observe a series of events and try to discover a rule that governs them. Once a rule is discovered, scientists can extrapolate from the rule to formulate theories of the observed and yet to be observed phenomena. One example is using inductive reasoning in the discovery that a certain type of bacterium is a cause of many ulcers.

Another common type of inductive reasoning is to map a feature of one member of a category to another member of a category. This is called categorical induction. This type of induction projects a known property of one item onto another item from the same category. Thus, knowing that the Rous Sarcoma virus is a retrovirus that uses RNA rather than DNA, a biologist might assume that another virus that is thought to be a retrovirus also uses RNA rather than DNA. Although research on this type of induction typically has not been discussed in accounts of scientific thinking, this type of induction is common in science.

Turning now to deductive thinking, many thinking processes to which scientists adhere follow traditional rules of deductive logic. These processes correspond to conditions in which a hypothesis may lead to, or is deducible to, a conclusion. Although they are not always phrased in syllogistic form, deductive arguments can usually be phrased as “syllogisms,” or as brief mathematical statements in which the premises lead to the conclusion. Deductive reasoning is an extremely important aspect of scientific thinking because it underlies a large component of how scientists conduct their research. By looking at many scientific discoveries, we can often see that deductive reasoning is at work. Deductive reasoning statements all contain information or rules that state an assumption about how the world works and a conclusion that would necessarily follow from the rule.

Inductive and deductive reasoning, even by successful scientists, is not immune to error. Two classes of errors commonly found in deductive reasoning are context and content errors. A common context error that people often make is to assume that conditional relationships are, in fact, biconditional. The conditional statement “if someone has AIDS then they also have HIV,” for example, does not necessarily imply that “if someone has HIV then they also have AIDS.” This is a common error in deductive reasoning that can result in logically incorrect conclusions being drawn. A common content error people often make is to modify the interpretation of a conclusion based on the degree to which the conclusion is plausible. Here, scientists may be more likely to accept a scientific discovery as valid if the outcome is plausible. You can see how this second class of errors in deductive logic can have profound implications for theory development. Indeed, if scientists are overly blinded by the plausibility of an outcome, they may fail to objectively evaluate the steps in their deductive process.

One of the most widely mentioned reasoning processes used in science is analogy. Scientists use analogies to form a bridge between what they already know and what they are trying to explain, understand, or discover. In fact, many scientists have claimed that the use of certain analogies was instrumental in their making a scientific discovery, and almost all scientific autobiographies and biographies feature an important analogy that is discussed in depth. Coupled with the fact that there has been an enormous research program on analogical thinking and reasoning, we now have a number of models and theories of analogical reasoning that show exactly how analogy can play a role in scientific discovery.

Traditional accounts of analogy distinguish between two components of analogical reasoning – the target and the source. The target is the concept or problem that a scientist is attempting to explain or solve. The source is another piece of knowledge that the scientist uses to understand the target, or to explain the target to others. What the scientist does when he or she makes an analogy is to map features of the source onto features of the target. By mapping the features of the source onto the target, new features of the target may be discovered, or the features of the target can be rearranged so that a new concept is invented and a scientific discovery is made.

The process of making an analogy involves a number of key steps – retrieval of a source from memory, aligning the features of the source with those of the target, mapping features of the source onto those of the target, and possibly making of new inferences about the target. Scientific discoveries are made when the source highlights a hitherto unknown feature of the target or restructures the target into a new set of relations. Interestingly, research on analogy has shown that participants do not easily use analogy. Participants tend to focus on the sharing of a superficial feature between the source and the target, rather than the relations among features.

Many researchers have noted that an important component of science is the generation of new concepts and modification of existing ones. Scientific concepts, like all concepts, can be characterized as containing representations of words, thoughts, actions, objects, and processes. How does one’s knowledge of scientific concepts change over time? The large-scale changes that occur in conceptual structures have been labeled conceptual change. Theories of conceptual change focus on two main types of shifts. One is the addition of knowledge to a pre-existing conceptual structure. Here, there is no conflict between the pre-existing conceptual knowledge and the new information the student is acquiring. Such minor conceptual shifts are relatively easy to acquire and do not demand restructuring of the underlying representations of scientific knowledge. The second type of conceptual shift is what is known as “radical conceptual change”. In this type of situation, it is necessary for a new conceptual system to be acquired that organizes knowledge in new ways, adds new knowledge, and results in a very different conceptual structure. This radical conceptual change is thought to be necessary for acquiring many new concepts in physics and is regarded as the major source of difficulty for students. The factors at the root of this conceptual shift view have been difficult to determine, although a number of studies in human development, in the history of science, and in physics education give detailed accounts of the changes in knowledge representation that occur when people switch from one way of representing scientific knowledge to another.

One area in which students show great difficulty in understanding scientific concepts is in physics. Analyses of students changing conceptions, using interviews, verbal protocols, and behavioral outcome measures indicate that large-scale changes in students’ concepts occur in physics education. Following Kuhn, researchers have noted that students’ changing conceptions are similar to the sequences of conceptual changes in physics that have occurred in the history of science. These notions of radical paradigm shifts and ensuing incompatibility with past knowledge states have drawn interesting parallels between the development of particular scientific concepts in children and in the history of physics.

Overall, accounts of conceptual change in individuals indicate it is, indeed, similar to that of conceptual change in entire scientific fields. Individuals need to be confronted with anomalies that their pre-existing theories cannot explain before entire conceptual structures are overthrown. However, replacement conceptual structures have to be generated before the old conceptual structure can be discarded. Often, people do not overthrow their naive conceptual theories and have misconceptions in many fundamental scientific concepts that are maintained across the lifespan.

One important question concerns the extent to which ordinary thinking in nonscientific contexts and scientific thinking recruit similar versus disparate neural structures of the brain. Dunbar proposed that scientific thinking uses the same cognitive mechanisms all human beings possess, rather than being an entirely different type of thinking. He has proposed that in scientific thinking, standard cognitive processes are used, but are combined in ways that are specific to a particular aspect of science or a specific discipline of science. By comparing the results of brain imaging investigations of scientific thinking with brain imaging studies of nonscientific thinking, we can see both whether and when common versus dissociated brain sites are invoked during different cognitive tasks. This approach will make it possible to articulate more clearly what scientific thinking is and how it is both similar to and different from the nonscientific thinking typically examined in the cognitive laboratory.

Another recent shift in the use of computers in scientific discovery is to have computers and people make discoveries together, rather than expecting computers to make an entire scientific discovery. Now, instead of using computers to mimic the entire scientific discovery process used by humans, computers can use powerful algorithms that search for patterns on large databases and provide the patterns to humans who can then use the output of these computers to make discoveries from the human genome to the structure of the universe.

What happens during collaborative scientific thinking is that there is usually a triggering event, such as an unexpected result or situation that a student does not understand. This results in other members of the group adding new information to the person’s representation of knowledge, often adding new inductions and deductions that both challenge and transform the reasoner’s old representations of knowledge. This means that social mechanisms play a key component in fostering changes in concepts that have been ignored in traditional cognitive research but are crucial for both science and science education. In science education, there has been a shift to collaborative learning, particularly at the elementary level, but in university education, the emphasis is still on the individual scientist. Because many domains of science now involve collaborations across scientific disciplines, we expect the explicit teaching of collaborative science heuristics to increase.

Learning To Think: The Challenges of Teaching Thinking, R. Ritchhart, D. Perkins

The idea that thinking can be taught, or at least productively nurtured along its way, is ancient. Beginning with the efforts of Plato and the introduction of Socratic dialog, we see attention to improving intelligence and promoting effective thinking as a recurring educational trend throughout the ages. Early in the twentieth century, Dewey again focused North American’s attention on the importance of thinking as an educational aim. At the same time, Selz was advocating the idea of learnable intelligence in Europe. In the 1970s and 1980s, specific programs designed to teach thinking took shape, many of which continue in schools today. Efforts to teach thinking have proliferated in the new millennium, often becoming less programmatic in nature and more integrated within the fabric of schools.

Although it is true that the human mind comes readily equipped for a wide variety of thinking tasks, it is equally true that some kinds of thinking run against these natural tendencies. For example, probabilistic thinking is often counterintuitive in nature or doesn’t fit well with our experience. We have a natural tendency toward favoring our own position and interests – my-side bias – that can lead to poor conclusions in decision making and discernments of truth. We frequently draw conclusions and inferences based on limited evidence. The fundamental attribution error names the tendency, particularly in Westerners, to ascribe characterological traits to others based on limited but highly salient encounters.

Furthermore, sometimes our naturalways of making sense of the world actually stand in the way of more effective ways of thinking. For instance, our ability to focus attention can lead to narrowness of vision and insight. Our natural tendency to detect familiar patterns and classify the world can lock us into rigid patterns of action and trap us in the categories we invent. Relatedly, already developed understandings constitute systems of knowledge that are much more readily extended than displaced:We tend to dismiss or recast challenges rather than rethinking our understandings, which is a deep and general problem of learning. Our emotional responses to situations can easily override more deliberative thinking. The phenomenon of groupthink, in which the dominant views of the group are readily adopted by group members, can lead to limited processing and discernment of information. These are just a few thinking shortfalls suggesting that truly good thinking does not automatically develop in the natural course of events.

Our ability to see patterns and relationships forms the basis for inductive reasoning, but the latter requires a level of precision and articulation that must be learned. Our natural ability to make inferences becomes much more sophisticated through systematized processes of reasoning with evidence, weighing evidentiary sources, and drawing justifiable conclusions. Indeed, for most thinking abilities that might be considered naturally occurring, one can usually identify a more sophisticated form that such thinking might take with some deliberate nurturing. This type of thinking is what is often referred to as high-end thinking or critical and creative thinking. Such thinking extends beyond a natural processing of the world into the realm of deliberative thinking acts aimed at solving problems, making decisions, and forming conclusions.

The problems of overcoming thinking shortfalls while enhancing native thinking processes through education therefore constitute an important rationale for the explicit teaching of thinking. Furthermore, as knowledge and information become at the same time more complex and more accessible, critics argue that teaching thinking should be considered even more of a priority. In this setting, it is not enough to simply consume predigested knowledge, one must also become a knowledge builder and problem solver.

The first challenge relates to the bottom line: Can thinking be taught with some reasonable signs of success? The second challenge concerns what is meant when one talks about good thinking. Programs and efforts to teach thinking are shaped largely by the answer to this question. The third challenge deals with the dispositional side of thinking, not just skills and processes but attitudes and intellectual character. The fourth challenge is that of transfer, a pivotal concern within the teaching of thinking. We conclude with a fifth challenge, that of creating cultures of thinking, in which we examine the social context and environment in which thinking is being promoted. Each of these challenges involves key philosophical and practical issues that all efforts to teach thinking, whether undertaken by a single teacher or a major research university, must confront. We review the ways in which various efforts to teach thinking address these challenges to clarify just what is involved in teaching thinking.

In looking for success, it is helpful to bear in mind three broad criteria – magnitude, persistence, and transfer. An intervention appears successful to the extent that it shows some magnitude of impact on learners’ thinking with effects that persist well beyond the period of instruction and with transfer to other contexts and occasions. Previous reviewers of thinking programs pointed out that the empirical evidence needed to assess program effectiveness is often hard to come by in the research literature, often because of the lack of funding for careful long-term program evaluation. We emphatically do not limit this article only to those programs receiving extensive evaluation, but we do focus this section on a few such programs. The good news is that the history of efforts to teach thinking provides proofs for achieving all three criteria, at least to some extent.

Any program that aspires to teach thinking needs to face the challenge of defining good thinking, not necessarily in any ultimate and comprehensive sense but at least in some practical, operational sense... To begin, it is useful to examine some general notions about the nature of good thinking. There are a number of very broad characterizations. Folk notions of intelligence, in contrast with technical notions, boil down to good thinking. A number of years ago, Sternberg et al. reported research synthesizing the characteristics people envision when they think of someone as intelligent. Intelligent individuals reason systematically, solve problems well, think in a logical way, deploy a good vocabulary, make use of a rich stock of information, remain focused on their goals, and display intelligence in practical as well as academic ways. Perkins summed up a range of research on difficulties of thinking by noting the human tendency to think in ways that are hasty (impulsive, insufficient investment in deep processing and examining alternatives), narrow (failure to challenge assumptions, examine other points of view), fuzzy (careless, imprecise, full of conflations), and sprawling (general disorganization, failure to advance or conclude).

One common approach to defining good thinking is to characterize concepts, standards, and cognitive strategies that serve a particular kind of thinking well. These guide performance as norms and heuristics. When people know the norms and heuristics, they can strive to improve their practice accordingly. The result is a kind of “craft” conception: Good thinking is a matter of mastering knowledge, skills, and habits appropriate to the kind of thinking in question as guided by the norms and heuristics. Norms provide criteria of adequacy for products of thinking such as arguments or grounded decisions. Examples of norms include suitable conditions for formal deduction or statistical adequacy, formal (e.g., affirming the consequent) or informal (e.g., ad hominem argument) fallacies to be avoided, or maximized payoffs in game theory.

To summarize, the characteristic pedagogy of the approach through norms and heuristics follows from its emphasis on thinkers’ theories of action. Programs of this sort typically introduce norms and heuristics directly, demonstrate their application, and engage learners in practice with a range of problems, often with an emphasis on metacognitive awareness, self-management, and reflection on the strategies, general character, and challenges of thinking.

Models of intelligence with components offer more toward a theory of action. J. P. Guilford’s Structure of Intellect (SOI) model, for example, proposes that intelligence involves no fewer than 150 different components generated by a three-dimensional analysis involving several cognitive operations (cognition, memory, evaluation, convergent production, divergent production) crossed with several kinds of content (behavioral, visual figural, and more) and cognitive products (units, classes, relations, and more). An intervention developed by Meeker aims to enhance the functioning of a key subset of these components. Feuerstein argues that intelligence is modifiable through mediated learning (with a mediator scaffolding learners on the right kinds of tasks). His Instrumental Enrichment program offers a broad range of mediated activities organized around three broad categories of cognitive process – information input, elaboration, and output – to work against problems such as blurred and sweeping perception, impulsiveness, unsystematic hypothesis testing, and egocentric communication.

Another approach to defining good thinking looks to models of human development that outline how cognitive development normally advances, often through some sequence of stages that represent plateaus in the complexity of cognition, as with the classic concrete and formal operational stages of Inhelder and Piaget.

The general pedagogical style of the developmental approach is to harness “natural” footholds and mechanisms of development to accelerate and perhaps reach levels that the learner otherwise would not attain. As theories of action, models of human development, like models of intelligence, do not so much offer strategic advice to learners as they address teachers and especially designers, suggesting how they might arrange activities and experiences that will push development forward. Indeed, a common, although questionable, tenet of much developmental theory is that you cannot teach directly the underlying logical structures. Learners must attain them by wrestling with the right kinds of problems under appropriately reflective and supportive conditions.

Most views of thinking are abilitiescentered, but several scholars have developed dispositional perspectives – for instance Dewey, who wrote of habits of mind; Baron as part of his searchinference framework; Ennis and Norris as part of analyses of critical thinking; Langer, with the notion of mindfulness, which she defined as “an open, creative, and probabilistic state of mind”; and Facione et al. Models of self-regulation have emphasized volitional aspects of thinking and individuals’ motivation to engage thoughtfully. We and our colleagues have done extensive work in this area, referring to intellectual character as a particular perspective on dispositions and to dispositions themselves. Accordingly, it is important to examine the dispositional side of the story and appraise its importance in the teaching of thinking.

Even when we sense opportunities for deeper thinking in principle, there are many reasons why we often shun them – blinding confidence in one’s own view, obliviousness to the possibilities for seeing things differently, aversion to complexities and ambiguities, and the like. Such lapses seem all too common, which is why, for example, Dewey emphasizes the importance of good habits of mind that can carry people past moments of distraction and reluctance. Scheffler, writing about cognitive emotions, put the point eloquently in stating that “emotion without cognition is blind, and . . . cognition without emotion is vacuous.”

It also is notable that the everyday language of thinking includes a range of terms for positive and negative dispositional traits considered to be important:Aperson may be open-minded or closed-minded, curious or indifferent, judicious or impulsive, systematic or careless, rational or irrational, gullible or skeptical. Such contrasts have more to do with how well people actually use their minds than how well their minds work.

Research on dispositional constructs such as the need for cognitive closure and the need for cognition (describing an individual’s tendency to seek, engage in, and enjoy cognitively effortful activity) has shown that they influence when and to what extent individuals engage in thinking and has demonstrated test–retest reliability. Measures of an individual’s need for cognition developed by Cacioppo and colleagues show that it is a construct distinguishable from ability.

Dweck and colleagues investigated another dispositional construct for a number of years – the contrast between entity learners and incremental learners. Broadly speaking, learners with an entity mindset believe that “you either get it or you don’t,” and if you don’t, you probably are not smart enough. As a result, they tend to quit in the face of intellectual challenges. In contrast, learners with an incremental mindset believe their abilities can be extended through step-by-step effort, so they persist. An extended program of research has shown that these traits are independent of cognitive abilities but often affect cognitive performance greatly. Also, teaching style and classroom culture can shape the extent to which students adopt entity versus incremental mindsets.

Although most scholars view dispositions as motivating thinking, we have analyzed the dispositional side of thinking into two components – sensitivity and inclination. Sensitivity does not motivate thinking as such but concerns whether a person notices occasions in the ongoing flow of events that might call for thinking, such as noticing a hasty causal inference, a sweeping generalization, a limiting assumption to be challenged, or a provocative problem to be solved. Inclination concerns whether a person is inclined to invest effort in thinking the matter through because of curiosity, personal relevance, and so on.

The question remains what role attention to dispositions does – and should – play in the teaching of thinking. Most programs do not attend directly and systematically to dispositional aspects of thinking, although they may foster dispositions as a side-effect. Indeed, it is inconvenient to address dispositions through programs that focus on direct instruction and regimens of practice. The dispositional side of thinking concerns noticing when to engage thinking seriously, which inherently does not come up in abilitiescentered instruction that point-blank directs students to think about this or that problem using this or that strategy. One solution to this suggests that culture is the best teacher of dispositions. A culture in the classroom, the family, or the workplace that foregrounds values of thinking and encourages attention to thinking would plausibly instill the attitudes and patterns of alertness called for.

In summary, both folk psychology and a good deal of academic psychology give abilities center stage in explaining good and not-so-good thinking and thinkers. Along with this abilities-centered view of thinking comes a concomitant view of what it is to teach thinking: To get people to think better and improve their abilities, teach problem-solving skills, learning skills, selfmanagement skills, and so on. All this certainly has value as far as it goes. However, the arguments advanced here question the completeness of the storyline. They challenge whether performance-on-demand tasks are a good model of how thinking works in everyday life and urge that well-rounded efforts to teach thinking attend to dispositional development as well as the development of abilities.

Like education in general, efforts to teach thinking do not simply target the here and now: They mean to serve the there and then. What learners acquire today in the way of thinking skills, strategies, cognitive schemata, underlying cognitive operations, dispositions, metacognitive capabilities, and the like aims to help them there and then make a difficult personal decision or study quantum physics or manage a business or draft and deliver a compelling political statement. In other words, the teaching of thinking reaches for transfer of learning. Sometimes the ambition for transfer is modest – experiences with reading for understanding or mathematical problem solving here and now should improve performance for the same activities later in other contexts. Not uncommonly, however, the ambition is far more grand – fundamental and far-reaching transformation of the person as a thinker.

Although it might be thought that skilled cognition reflects general cognitive capabilities, an extensive body of research has shown the fundamental importance of familiarity with the knowledge, strategies, values, challenges, and other features of particular disciplines and endeavors.

Evidence from a range of professions argues that naturalistic decision-making depends on quick typing of situations to link them to prototypical solutions that can be adjusted to the immediate circumstances. In the same spirit, path analyses of performance in practical job contexts has shown specific knowledge to be a much more direct predictor of performance than general intelligence. Several scholars have argued that intelligent behavior is deeply context bound. Effective thinking depends so much on a large repertoire of reflexively activated, context-specific schemata that substantial transfer of expert thinking from one domain to another is impossible. Everyday support for this comes from the informal observation that people rarely manage to display highlevel thinking in more than one field.

Accordingly, complex cognition is more likely to develop through “cognitive apprenticeship” in the context of rich social and physical support than through instruction that attempts to teach abstract schemas. Within such environments, individuals may first participate on the periphery of the group or with high-levels of support and gradually progress to more independent and central forms of operation as their expertise and comfort level increases. Because cognition is so situated, the story goes, it is hard to uproot patterns of cognition and transplant them into very different contexts where they can still thrive.

In summary, we suggest that the debate around transfer, expertise, and situated learning has been overly polarized and ideological, leading to sweeping declarations on both sides regarding what is possible or impossible that do not stand up to empirical examination. The relationship between general cognitive structures and particular situations perhaps needs to be understood as more complex and dynamic. Perkins and Salomon offer the analogy of the human hand gripping something. The human hand plainly is a very flexible general instrument, but it always functions in context, gripping different things in different ways. Moreover, we need to learn to grasp objects according to their affordances: You don't hold a baby the same way you hold a brick. Likewise, one can acknowledge a broad range of general strategies, cognitive operations, and schemata without naively holding that they operate in context-neutral ways. Adjustments are always made – sometimes easily, sometimes with difficulty. Skilled cognition involves complex interarticulations of the general and the specific.

Culture has been mentioned briefly in previous sections, but one still might ask: What is it about culture, and cultures of thinking in particular, that demands attention? Three important motives are worthy of attention: First, the supporting structures of culture are needed to sustain gains and actualize intelligent behavior over time, as opposed to merely building short-term capacity. It is through the culture of the classroom that strategies and practices take on meaning and become connected to the work of learning. Second, culture helps to shape what we attend to, care about, and focus our energies upon. Thus, culture is integrally linked to the dispositional side of thinking and to the cultivation of inclination and sensitivity. Third, researchers and program developers increasingly have recognized that thinking programs are not merely implemented but are enacted, developed, and sustained in a social context. As a result, they have found it necessary to move away from teacher-proof materials, which view learning as an isolated individual process, and toward approaches that pay more attention to the underlying conditions of learning.

Culture, construed broadly, refers to the context and general surround in which we operate. This doesn’t tell us much about what it means to become enculturated, however. To illuminate this issue it is helpful to look at particular intellectual subcultures or communities of practice, say of mathematicians or writers or even mechanics. What does it mean to be a part of these cultures? A frame that we have found useful is based on two top-level conceptions: resources and practice. Resources are the things upon which members of the culture of practice draw when they do their work. Resources can be physical in nature: computers, books, instruments, tools, and the like. There are also social resources such as colleagues, coworkers, editors, peer-review boards, and so on. These types of resources help distribute cognition outside the individual thinker’s mind. In addition, there are conceptual resources consisting of the conceptual, knowledge, and belief systems in which the subculture readily traffics. Also included in the conceptual resources are the symbol systems and notational structures evolved to support abstract thought.

Practice captures the constructive acts engaged in by the cultural group – what it is they do, the kind of work that is valued and rewarded, the methods they employ. This connects the group to the socio-historically valued ways of knowing and thinking, such as the epistemic forms of the disciplines that are part of the group’s heritage. Resources and practice interact dialectically in that individual and group practice transform resources that, in turn, have an effect on practice. At the same time, resources and practice provide supports for distributed intelligence, scaffolding intelligent behavior beyond that which can be displayed by an individual mind.

But, how does this enculturation happen? How are a culture’s practice and resources conveyed and learned by group members? In a study of thoughtful classrooms, Ritchhart identified seven cultural forces at work in classrooms that facilitated the process of enculturation in thinking: (1 ) messages from the physical environment about thinking, (2) teacher modeling of thinking and dispositions, (3 ) the use of language of thinking, (4) routines and structures for thinking, (5 ) opportunities created for thinking, (6) conveyance of expectations for thinking, and (7) interactions and relationships supportive of thinking.

Ultimately, teaching students to be more metacognitive and reflective, providing rich opportunities for thinking across various contexts, setting up an environment that values thinking, and making the thinking of group members visible contribute a great deal to the formation of a culture of thinking. The cultural forces can be leveraged toward this end. Within such a culture of thinking, other efforts to teach thinking, both formal and informal, have a greater likelihood of taking hold because they will be reinforced through the culture and opportunities for transfer and reflection will increase. In summary, in some sense, a fully developed culture of thinking in the classroom or, indeed, in other settings such as the home or the workplace, represents the cohesive culmination of the separate challenges of achieving results, defining the thinking, attaining transfer, and attending to thinking dispositions. A thoroughgoing culture of thinking attends to all of these.

We showed how the effective teaching of thinking is more than just the development of ability, demanding the development of awareness and inclination as well. In particular, the lack of a sensitivity to occasions for thinking appears to be a major bottleneck when it comes to putting one’s abilities into action.

Transfer, a pivotal concern within the teaching of thinking, constituted our fourth challenge. Although some have argued that transfer cannot be obtained because all knowledge is bound to context, the empirical record of successful programs has shown clearly that some degree of transfer is possible across domains of content knowledge. This is by no means automatic, however. Transfer must be designed deliberately into interventions by highlighting key features of the situation that need attention, promoting reflective abstraction of underlying principles, and providing practice across multiple contexts. Even then, one is more likely to see near transfer of thinking to similar contexts than far transfer.

Our fifth challenge, that of creating cultures of thinking, examined the social context and environment in which thinking is fostered. Efforts to teach thinking cannot be removed from their social context. Context provides important avenues for the development of supporting inclinations toward thinking, learning from more accomplished peers, focusing attention, and access to the resources and practices of the group. In classrooms, a set of cultural forces directs and shapes students’ learning experiences both directly and indirectly. These cultural forces convey to students how much and what kinds of thinking are valued, what methods the group uses to go about thinking, and what expectations there are regarding thinking. Furthermore, the thinking of individuals and groups is made visible through these forces.

Perhaps the biggest question about the teaching of thinking concerns how to integrate it with other practices, in school and out of school, in an effectiveway.We already know enough about the teaching of thinking to have a substantial impact, and yet the reality of collective practice falls short. We must ask ourselves: How can thinking initiatives be sustained and integrated with the many other agendas faced by schools, museums, clubs, corporate cultures, and other settings in which thinking might thrive?

Practical Aspects of Theoretical Reasoning, G. Harman

Practical reasoning in the more or less technical sense leads to (or modifies) intentions, plans, and decisions. Theoretical reasoning in the corresponding technical sense leads to (or modifies) beliefs and expectations. There is also the possibility that reasoning of either sort leaves things unchanged.

Nevertheless, there is a difference between theoretical reasoning and practical reasoning and a corresponding difference between theoretical reasons and practical reasons. In particular, there is a distinction between theoretical reasons to believe something and practical reasons to believe something. For example, Samantha has theoretical reasons to believe that knowledge of the history of philosophy is not very useful in actually doing good philosophy today, reasons based on a careful study of the history of philosophy and of the best recent philosophical literature. On the other hand, she has practical reasons to believe that knowledge of the history of philosophy is very useful in actually doing philosophy today, because she wants to be hired by a philosophy department that has a policy of only hiring candidates who believe that a solid knowledge of the history of philosophy is very useful to anyone who tries to do philosophy today.

A purely theoretical reason to believe something is sometimes called an epistemic reason to believe it, in contrast with a nonepistemic practical reason. There are interesting questions about how and to what extent practical reasons might be relevant to theoretical reasoning, strictly so-called. Practical reasons are certainly relevant to whether to undertake theoretical reasoning about a particular subject. Practical considerations may also be reflected in the role played by conservatism and simplicity in theoretical reasoning.

Reasoning or inquiry is a process by which you change (or don’t change) your views. A theory of reasoning or inquiry is a descriptive or normative theory of that process. The theory of implication and consistency concerns abstract properties of propositions and abstract relations between propositions. That is not an especially normative subject and it does not have an especially psychological subject matter. We can meaningfully ask whether the theory of implication and consistency has any special relevance to the theory of reasoning and inquiry, a question that is often hidden from view by the ambiguity of the term “logic.”

An argument or proof is an abstract structure of propositions, consisting of initial premises, intermediate steps, and final conclusion. A formal system of proof might state certain misnamed “rules of inference” and require that each step in an argument should either be a premise or should follow from previous steps in accordance with one of the so-called rules of inference. Such “rules” are about implication, not inference, and they are “rules” only in the sense that they are constraints on what structures count as formal arguments in that system. They are rules that proofs must satisfy, not rules for reasoners to follow.

A valid proof or argument shows some of the implications of the premises. Of course, the premises imply themselves, so a typical proof shows additional implications. Reasoning, on the other hand, does not just add further conclusions to things you already accept. It typically also involves giving up some of things previously accepted. If we describe what you initially accept as “premises,” then we have to say that reasoning often involves abandoning premises and not just accepting further conclusions.

A first approximation theoretical reasoning is concerned with deciding what to believe and practical reasoning is concerned with deciding what to do. To a second approximation, we can say that theoretical reasoning is a process by which in the first instance you change your beliefs and expectations and that practical reasoning is a process by which in the first instance you change your choices, plans, and intentions.We have to say something like “in the first instance” because changing what you plan to do can affect what you believe will happen and changing your beliefs may lead you to change your plans.

But there are also important differences between theoretical and practical reasoning. A very important difference has to do with wishful thinking, which is perfectly proper in practical reasoning in a way that it is not proper in theoretical reasoning. Albert’s preference for the eastern route can give him a practical reason to take the eastern route rather than the western route. But Betty’s preference for Albert to be taking the eastern route does not in the same way give her a theoretical reason to believe that he is taking the eastern route.

To reach a conclusion is, among other things, to conclude an investigation. Practical reasons are relevant to reaching a conclusion, at least to the extent that they are relevant to whether to stop devoting resources to that investigation. This is not to say that practical reasons can properly be used to decide between several competing theoretical conclusions. But practical reasons can properly be relevant to whether to end inquiry, for example on the grounds that further investigation is not likely to be worth the effort.

Relevant factors in theoretical reasoning include conservatism, simplicity, and coherence. Roughly speaking, starting with an initial view, you try to retain as much as possible of that initial view (conservatism), to favor simpler over more complex hypotheses (simplicity), to reduce inconsistency (negative coherence), and to find explanations of things in which you are interested (positive coherence).

Someone might ask what justifies a reliance on such factors as conservatism, simplicity, and coherence in our theoretical reasoning. Perhaps such reliance involves the sort of wishful thinking that we normally suppose is not theoretically reasonable. Maybe it’s just that we want our present views to be correct and we don’t want to have to change our minds. And maybe we want the general principles and theories we accept to be relatively simple because we have an aesthetic preference for simplicity or because it is easier for us to use simpler theories.

Perhaps reliance on conservatism, simplicity, and coherence can be justified as promoting our goals, in the way that believing in the usefulness of the history of philosophy might promote Samantha’s goal of being hired by the Mooseton philosophy department. But then our reasoning would seem to be practical rather than theoretical, because the relevant considerations would be practical, not purely epistemic.

Still, we favor a simpler hypothesis over infinitely many more complicated hypotheses that do equally well or better at data coverage. We reason as if we believed that the simpler hypothesis is more likely to be correct in this case. But why should we believe this? Actually, we do not exactly “believe” this. Our preference for simplicity is “built into” our system of reasoning—as it were, part of our initial probability distribution. It is a basic aspect of our epistemic probability. Our inferential practice treats simpler hypotheses as more epistemically probable than corresponding more complex hypotheses that account equally well for the data.

Once we realize that we are influenced by simplicity in this way, we can ask whether we should continue to allow ourselves to be influenced. We can ask why we should go along with this tendency in our reasoning practices. One thing that seems relevant is that a reasoning system needs inductive bias if it is to reach any inductive conclusions at all. A system without inductive bias cannot learn from experience. Now, perhaps certain entities can survive without learning, but ordinary people cannot. Some bias that will enable learning has to be built into us somehow, perhaps as the result of evolution by natural selection.

Let us briefly look at an analogous issue concerning the role of conservatism in theoretical reasoning. Our reasoning is conservative in the sense that we start with our present view and try to improve it by getting rid of inconsistency and by increasing its coherence in ways that help us answer questions in which we are interested.

So, there is a further bias in reasoning beyond a simple inductive bias. This further bias favors beliefs that we already have over propositions that we do not already accept. Again we can ask whether we should acquiesce in this further conservative bias. An alternative idea would restrict the conservative bias to certain “foundational” beliefs, such as beliefs about your most immediate experience and beliefs based on the recognition of self-evident truths.

But there is a compelling argument for conservatism and against special foundationalism— namely that special foundationalism leads inevitably to scepticism, and that again one will not be able to learn much of anything if one cannot rely on one’s other nonfoundational beliefs. Here is another practical reason to acquiesce in a certain way of doing theoretical reasoning. Again, this sort of practical reason for an aspect of theoretical reasoning does not imply that theoretical reasoning itself is practical reasoning and it does not imply that theoretical reasoning involves wishful thinking because of its bias toward conservatism.

My brief conclusion is that, although wishful thinking is not relevant in theoretical reasoning in the way that it is relevant in practical reasoning, certain aspects of theoretical reasoning can be given a practical defense. That defense does not mean that wishful thinking is allowed internally to theoretical reasoning. The defense can also be given a nonpractical interpretation in terms of what conclusions ought to be reached.

Rationality and Psychology, R. Samuels, S. Stich

One quite plausible conclusion to draw from the experimental findings reported in the heuristics and biases literature is that (1) People’s intuitive judgments on a large number of reasoning and decision making problems regularly deviate from appropriate norms of rationality.

Kahneman and Tversky: (2) "Many of the instances in which our judgments and decisions deviate from appropriate norms of rationality are explained by the fact that, in making these judgments and decisions, people rely on heuristics like representativeness which sometimes yield reasonable judgments and sometimes lead to severe and systematic errors."

Though (1) and (2) have been challenged in a number of ways, they are both relatively modest reactions to the experimental findings. However, many writers have suggested a much stronger and more disturbing conclusion, which maintains that people use these heuristics because they have no better tools available for dealing with many reasoning and decision making problems. According to Slovic, Fischhoff and Lichtenstein, for example, “It appears that people lack the correct programs for many important judgmental tasks. . . . We have not had the opportunity to evolve an intellect capable of dealing conceptually with uncertainty”.

The hypothesis that the only cognitive tools available to most human reasoners and decision makers are “shoddy software” like the representativeness heuristic has been the main target of an important critique of the heuristics and biases tradition mounted by evolutionary psychologists. In this section we’ll give an overview of that critique. Though the interdisciplinary field of evolutionary psychology is too new to have developed any precise and widely agreed upon body of doctrine, there are three basic theses that are clearly central. The first is that the mind contains a large number of special purpose systems—often called “modules” or “mental organs.”

The second central thesis of evolutionary psychology is that, contrary to what has been argued by Fodor and others, the modular structure of the mind is not restricted to input systems (those responsible for perception and language processing) and output systems (those responsible for producing actions). According to evolutionary psychologists, modules also subserve many so-called central mental capacities such as reasoning, desire formation and decision making. The third thesis is that mental modules are adaptations— they were, as Tooby and Cosmides have put it, “invented by natural selection during the species’ evolutionary history to produce adaptive ends in the species’ natural environment”.

If much of central cognition is indeed subserved by cognitive modules that were designed to deal with the adaptive problems posed by the environment in which our primate forebears lived, then we should expect that the modules responsible for reasoning would do their best job when information is provided in a format similar to the format in which information was available in the ancestral environment.

Evolutionary psychologists have urged that their findings support the truth of three increasingly optimistic claims. First, they maintain, the data suggest that:(4) There are many reasoning and decision-making problems on which people’s intuitive judgments do not deviate from appropriate norms of rationality. Second, they have argued that: (5) Many of the instances in which our judgments and decisions accord with appropriate norms of rationality are to be explained by the fact that, in making these judgments, we rely on mental modules that were designed by natural selection to do a good job at nondemonstrative reasoning when provided with the sort of input that was common in the environment in which our hominid ancestors evolved. Finally, evolutionary psychologists have also on occasion issued exuberantly Panglossian proclamations suggesting that (6) Most or all of our reasoning and decision making is subserved by normatively unproblematic “elegant machines” designed by natural selection, and thus any concerns about systematic irrationality are unfounded.

Though this is not the place to defend our view in detail, we are inclined to think that the correct conclusions to draw about the rationality of ordinary folk from the large and growing body of experimental findings about reasoning and decision making are not nearly so optimistic as (6) nor nearly so pessimistic as (3).8 To begin, note that (1), which claims that people’s intuitive judgments on many reasoning and decision making problems deviate from appropriate norms of rationality, and (4), which claims that there are many reasoning and decision making tasks on which people’s intuitive judgments do not deviate from appropriate norms of rationality, are entirely compatible. Moreover, we believe that the evidence... make an overwhelmingly plausible case that both (1) and (4) are true. People do make serious and systematic errors on many reasoning tasks, but they also perform quite well on many others. The heuristics and biases tradition has focused on the former cases, while evolutionary psychologists have focused on the latter.

While (3) and (6) can’t both be true, they can both be false, and we believe they are. There is nothing in the heuristics and biases literature that supports the claim that problematic heuristics are the only reasoning resources people can draw on, nor does this literature provide us with any reason to think that normatively unproblematic mechanisms like those posited by evolutionary psychologists do not exist. On the other side, evolutionary psychologists certainly have offered no reason to think that all reasoning is subserved by normatively unproblematic modules. Indeed, if it is granted, as we think it should be, that people typically do poorly on a large and important class of reasoning problems, then it is clear that (6) is indefensible.

We believe that the “middle way” we’ve been urging between the pessimism suggested by the heuristics and biases tradition and the optimism proclaimed by evolutionary psychologists is compatible with and perhaps made more plausible by a family of dual processing theories about the mental mechanisms underlying reasoning and decision making that have gained increasing prominence in recent years. Though these theories differ from one another in many details, they all propose that reasoning and decision making are subserved by two quite different sorts of system. One system is fast, holistic, automatic, largely unconscious, and requires relatively little cognitive capacity. The other is relatively slow, rule based, more readily controlled, and requires significantly more cognitive capacity. Stanovich speculates that the former system is largely innate, emerged relatively early in human evolution and, as evolutionary psychologists suggest, has been shaped by natural selection to do a good job on problems like those that would have been important to our hominid forebears. The other system, by contrast, evolved more recently and, “although its overall function was no doubt fitness enhancing, it is the primary maximizer of personal utility”. This newer system is more heavily influenced by culture and formal education and is often more adept at dealing with many of the problems posed by a modern, technologically advanced, and highly bureaucratized society.

If Stanovich and other dual process theorists are on the right track, then the unbridled optimism sometimes suggested by evolutionary psychologists is unwarranted, since most untutored people do indeed lack the capacity to deal with a wide range of problems that are important in a technological society. But the glum pessimism often associated with the heuristics and biases tradition is not warranted either. Since the fast, automatic, and evolutionarily older system requires little cognitive capacity, everyone has the capacity to deal rationally with many reasoning and decision making problems that were important in the environment in which we evolved. Moreover, since the new, slow, rule-based system can be significantly affected by education, there is reason to hope that better educational strategies will improve people’s performance on those problems that the old system was not designed to deal with.

Rationality and Science, P. Thagard

This chapter provides a review and assessment of central aspects of rationality in science. It deals first with the traditional question, What is the nature of the reasoning by which individual scientists accept and reject conflicting hypotheses? I will also discuss the nature of practical reason in science and then turn to the question of the nature of group rationality in science. The remainder of the chapter considers whether scientists are in fact rational, that is, whether they conform to normative standards of individual and group rationality. I consider various psychological and sociological factors that have been taken to undermine the rationality of science.

First, however, it is necessary to deal with a prior issue: What are the goals of science? In general, rationality requires reasoning strategies that are effective for accomplishing goals, so discussion of the rationality of science must consider what science is supposed to accomplish. To begin, we can distinguish between the epistemic and the practical goals of science. Possible epistemic goals include truth, explanation, and empirical adequacy. Possible practical goals include increasing human welfare through technological advances. My view is that science has all of these goals, but let us consider some more extreme views.

Some philosophers have advocated the view that the primary epistemic aim of science is the achievement of truth and the avoidance of error. On this view, science is rational to the extent that the beliefs that it accumulates are true, and scientific reasoning is rational to the extent that it tends to produce true beliefs. The philosophical position of scientific realism maintains that science aims for true theories and to some extent accomplishes this aim, producing some theories that are at least approximately true. In contrast, the position of antirealism is that truth is not a concern of science. One of the most prominent antirealists is Bas van Fraassen, who argues that science aims only for empirical adequacy: scientific theories should make predictions about observable phenomena but should not be construed as true or false. The antirealist view, however, is at odds with the practice and success of science. Most scientists talk and act as if they are trying to figure out how the world actually works, not just attempting to make accurate predictions. Moreover, the impressive technological successes of science are utterly mysterious unless the scientific theories that made them possible are at least approximately true.

But truth is not the only goal of science. The most impressive accomplishments of science are not individual facts or even general laws, but broad theories that explain a great variety of phenomena. For example, in physics the theory of relativity and quantum theory each provide understanding of many phenomena, and in biology the theory of evolution and genetic theory have very broad application. Thus a major part of what scientists strive to do is to generate explanations that tie together many facts that would individually not be very interesting. A scientist who aimed only to accumulate truths and avoid errors would be awash in trivialities. Hence science aims for explanation as well as truth. These two goals subsume the goal of empirical adequacy, because for most scientists the point of describing and predicting observed phenomena is to find out what is true about them and to explain them.

The major focus of the cognitive sciences such as psychology and neuroscience has been understanding the basic mechanisms of thinking, but there have also been practical motivations such as improving education and the treatment of mental illnesses. It is clear, therefore, that one aim of the scientific enterprise is the improvement of human welfare through technological applications. This is not to say that each scientist must have that aim, since many scientists work far from areas of immediate application, but science as a whole has made and should continue to make technological contributions.

Saying that the aims of science are truth, explanation, and human welfare does not imply that these aims are always accomplished, only that these are the aims that science generally does and should have. We can now address the question of what strategies of rational thinking best serve the accomplishment of these aims.

Popper argues that scientists should not aim for confirmation but should operate as the following sort of falsification agents. Scientists use hypotheses to make predictions, but their primary aim should be to find evidence that contradicts the predicted results, leading to the rejection of hypotheses rather than their acceptance. Hypotheses that have survived severe attempts to falsify them are said to be corroborated. On this view, the proponents of the collision theory of dinosaur extinction should attempt to falsify their theory by stringent tests and only then consider them as corroborated, but not as accepted as true.

Scientists are not just confirmation agents either, since hypotheses often get support not just from new predictions, but also from explaining data already obtained. Moreover, it often happens in science that there are conflicting hypotheses that are to some extent confirmed by empirical data. As Lakatos argues, the task then is not just to determine what hypotheses are confirmed, but also what hypotheses are better confirmed than their competitors. Hypothesis assessment is rarely a matter of evaluating a hypothesis with respect to its predictions, but rather requires evaluating competing hypotheses, with the best to be accepted and the others to be rejected.

If scientists are not confirmation, falsification, or probabilistic agents, what are they? One answer, which goes back to two nineteenth-century philosophers of science, William Whewell and Charles Peirce, is that they are explanation agents. On this view, what scientists do in theoretical inference is to generate explanations of observed phenomena, and a theory is to be preferred to its competitors if it provides a better explanation of the evidence. Theories are accepted on the basis of an inference to the best explanation. Such inferences are not merely a matter of counting which among competing theories explains more pieces of evidence, but also require assessment in terms of the overall explanatory coherence of each hypothesis with respect to a scientist’s whole belief system. Factors that go into this assessment for a particular hypothesis include the evidence that it explains, its explanation by higher-level hypotheses, its consistency with background information, its simplicity, and analogies between the explanations offered by the hypothesis and explanations offered by established explanations.

I prefer to view scientists as explanation agents rather than as confirmation, falsification, or probabilistic agents because this view fits better with the historical practice of scientists as evident in their writings, as well as with psychological theories that are skeptical about the applicability of deductive and probabilistic reasoning in human thinking. But I acknowledge that the probabilistic agent view is probably the most popular one in contemporary philosophy of science; it has largely absorbed the confirmation agent view by the plausible principle that evidence confirms a hypothesis if and only if the evidence makes the hypothesis more probable.

As with practical judgments of emotional coherence in practical decision making, we have no direct conscious access to the cognitive processes by which we judge some hypotheses to be more coherent than others. What emerges to consciousness from a judgment of explanatory coherence is often emotional, in the form of liking or even joy with respect to one hypothesis, and dislike or even contempt for rejected competing hypotheses...Emotional inputs to hypothesis evaluation include the varying attitudes that scientists hold toward different experimental results and even for different experiments—any good scientist knows some experiments are better than others. Another kind of emotional input is analogical: a theory analogous to a positively viewed theory such as evolution will have greater positive valence than one that is analogous to a scorned theory such as cold fusion.

What are the mechanisms of valence exchange—that is, how do people pass their emotional values on to other people? Two relevant social mechanisms are emotional contagion and attachment-based learning. Emotional contagion occurs when person A expresses an emotion and person B unconsciously mimics A’s facial and bodily expressions and then begins to acquire the same emotion. For example, if a group member enthusiastically presents a research strategy, then the enthusiasm may be conveyed through both cognitive and emotional means to other members of the group. The cognitive part is that the other group members become aware of possible actions and their potential good consequences, and the emotional part is conveyed by the facial expressions and gestures of the enthusiast, so that the positive valence felt by one person spreads to the whole group. Negative valence can also spread, not just from a critic pointing out drawbacks to a proposed action as well as more promising alternatives, but also by contagion of the negative facial and bodily expressions.

Another social mechanism for valence exchange is what Minsky calls attachment-based learning. Minsky points out that cognitive science has developed good theories of how people use goals to generate subgoals, but has had little to say about how people acquire their basic goals. Similarly, economists employing the expected-utility model of decision making take preferences as given, just as many philosophers who hold a belief-desire model of rationality take desires as given. Minsky suggests that basic goals arise in children as the result of praise from people to whom the children are emotionally attached. For example, when young children share their toys with their playmates, they often receive praise from their parents or other caregivers. The parents have positive valence for the act of sharing, and the children may also acquire a positive emotional attitude toward sharing as the result of seeing that it is something cared about by people whom they care about and who care about them. It is not just that sharing becomes a subgoal to accomplish the goal of getting praised by parents; rather, being kind to playmates becomes an internalized goal that has intrinsic emotional value to the children.

I conjecture that attachment-based learning also occurs in science and other contexts of group decision making. If your supervisor is not just a boss but also a mentor, then you may form an emotional attachment that makes you particularly responsive to what the supervisor praises and criticizes. This makes possible the attachment-based transmission of positive values such as zeal for truth and understanding, or, more locally, for integrity in dealing with data and explanations.

There may, however, be quasi-verbal mechanisms for valence transfer. Thagard and Shelley discuss emotional analogies whose purpose is to transfer valences as well as verbal information. For example, if a scientist presents a research project as analogous to a scientific triumph such as the asteroid theory of dinosaur extinction, then listeners may transfer the positive value they feel for the asteroid theory to the proposed research project. Alternatively, if a project is analogous to the cold fusion debacle, then the negative valence attached to that case may be projected onto the proposed project. Thus emotional analogies are a third mechanism, in addition to emotional contagion and attachment-based learning, for transfer of valences.

A person or group is rational to the extent that its practices enable it to accomplish its legitimate goals. At the beginning of this chapter, I argued that the legitimate goals of science are truth, explanation, and technologies that promote human welfare. Do scientific individuals and groups function in ways that further these goals, or do they actually pursue other personal and social aims that are orthogonal or even antagonistic to the legitimate goals? I will now consider several psychological and sociological challenges to the rationality of science.

A more serious challenge to the rationality of science comes from hot cognition. Like all people, scientists are emotional beings, and their emotions may lead to distortions in their scientific works if they are attached to values that are inimical to the legitimate aims of science. Here are some kinds of cases where emotions have distorted scientific practice: 1. Scientists sometimes advance their own careers by fabricating or distorting data in order to support their own hypotheses. In such cases, they have greater motivation to enhance their own careers than to pursue truth, explanation, or welfare. 2. Scientists sometimes block the publication of theories that challenge their own by fabricating problems with submitted articles or grant proposals that they have been asked to review. 3. Without being fraudulent or intentionally evil, scientists sometimes unintentionally deceive themselves into thinking that their hypotheses and data are better than those of their rivals. 4. Scientists sometimes further their careers by going along with politically mandated views—for example, the Nazi rejection of Einsteinian physics and the Soviet advocacy of Lysenko’s genetic theories.

It is important to recognize, however, that the natural emotionality of scientists is not in itself a cause of irrationality. As I documented elsewhere, scientists are often motivated by emotions that further the goals of science, such as curiosity, the joy of discovery, and appreciation of the beauty of highly coherent theories. Given the modest incentive structure of science, a passion for finding things out is a much more powerful motivator of the intense work required for scientific success than are extrinsic rewards such as money and fame. Thus hot cognition can promote scientific rationality, not just deviations from it. The mobilization of resources and allies can be in the direct or indirect service of the aims of science, not just the personal aims of individual scientists.

Educators and Expertise: A Brief History of Theories and Models, R. Amirault, R. Branson

This chapter presents a brief historical account of educators' views about the nature of expertise and the roles experts have played in educational models to improve human performance. We provide a listing of historically relevant educators and a descriptive summary of the various learning theories and mechanisms advocated as fundamental components of high skill development. We also describe some of the methods used through history by which expertise and expert performance have been assessed from an educational standpoint.

In many historical writings, for example, terms such as "masters," "teachers," and "professors" are commonly used to denote highly skilled individuals, and any referent to "expertise" is often general in nature. The empirical descriptions provided by systematic investigation into the mechanisms underlying expertise and expert performance did not begin to appear in the historical account until the late nineteenth century, when operationalized definitions for performance phenomena were first developed and tested by the pioneering psychologists of that era. The lack of empirical specificity in the earlier record does not preclude, however, the review and synthesis of either the role experts have played in past educational efforts or the historically prescribed techniques for the development of highly skilled performance. Rather, it requires that the historical investigator become attuned to terms, phrases, and descriptions that align with what today's theorists and practitioners might more precisely refer to as either "expertise" or "expert performance." It requires that the reader, too, be able to consider descriptions of past situations and individuals and recognize common threads in the historical record as it relates to all types and views of skills development.

As we shall see, the salient characteristic of the historical record over some two and a half millennia from Socrates (ca. 400 BC) to Gagne (ca. 1970 AD) is an increasingly constrained view toward the study and development of expertise. The earliest recorded educators, including Plato and Socrates, often viewed expertise in what can be described as a "whole man" approach, a holistic view that included aspects of knowledge, skills, and morality to achieve "virtue" in the learner. Medieval European educators, describing new educational programs such as the trivium and the quadrivium, and implementing those paradigms within novel institutions such as the cathedral schools and the university, constrained the focus of skills development to more specialized areas, including geometry and the Latin language, resulting in greater codification of educational systems and their attendant instructional techniques. In the most recent period, twentieth-century educational psychologists, working in scientifically based learning paradigms, further constrained the focus of skills development and expertise, specifying detailed and empirically based models for the acquisition of the highest levels of skill within highly specific domain areas (e.g., concert violin performance, professional golfing, and tournament-level chess competition). This trend, broad and imperfect as it may be, will nevertheless serve nicely to trace the general outlines of our history.

It is beneficial at the outset of our review to make note of some key historical trends that will be presented in this chapter and that have impacted educators' views of expertise throughout the centuries. Among these, we will see 1. The progression from largely individualized instruction in the ancient context to mass education in later periods (finding culmination in the mass production educational techniques of the nineteenth and twentieth centuries), 2. The progression of a model of education for the few in ancient times to education for the many after the Industrial Revolution (a function of the decreasing cost of educating a learner via mass production techniques), 3. The changing role of the instructor, juxtaposing at various points in history between subject matter expert and expert in educational techniques (reflecting current views on how to best achieve learning in students), and 4. A shift in skills assessment from informal and oral assessment in the ancient context to formal, objective, and measurable assessment in the Twentieth century (reflecting the increasing desire to objectively measure expertise). These trends, all of which can be seen in "seed" form in the ancient context, laid the foundation for, and sometimes the boundaries circumscribing, later attempts to study the nature and development of highly skilled individuals.

Education as a discipline has never suffered a shortage of divergent views, and it comes as little surprise that we immediately witness in the ancient period an early demarcation between two positions on its purpose: one that focused on the holistic development of the individual, and one that focused on applied skills building. These two early philosophies of education played a direct role in the manner in which expertise was defined and measured. Regardless of the position, however, the assumption was that the instructor should be an expert in the area in which he taught. This placed the teacher at the focal point of all education, with students building expertise via transmission from the expert, the instructor himself.

Socrates did not promote a formalized educational system consisting of schools that delivered and assessed learning outcomes; rather, he viewed education as a process of developing the inner state of individuals through dialogue and conversation. Now referred to as the Socratic method, the teacher employing this method would not transmit knowledge or practical skills (techne), but would engage the student in a dialogical process that brought out knowledge believed to be innate within the student. Instruction in the Socratic context, therefore, was conducted by means of interactive questioning and dialog, without concern for fixed learning objectives, and with the goal of developing "virtue" and achieving truth. Socrates similarly assessed his students via informal, dialectic questioning, his quest always to find some person who knew more than he.

Plato, generally sharing Socratic views, had some specific recommendations concerning the education of younger learners, which can be found in his classic work, The Republic. For example, Plato states that future Guardians of the State should pursue math-related studies for a period of ten years before advancement to subjects such as rhetoric or philosophy. Plato also emphasized the importance of abstract disciplines, such as philosophy and mathematics, but also believed that only a very few individuals possessed the "natural abilities" required for pursuit of such subjects. Thus, we witness in Plato an early belief in the presence of natural ability based on some form of genetic endowment, a prototypical concept foreshadowing all the way to Sir Francis Galton's nineteenth-century attempts to measure a generalized, inheritable intelligent quotient, g.

Socrates and Plato did not seem strongly concerned with the development of applied skills and actually seemed to demonstrate an aversion to practical skills training when devoid of what they viewed as the deeper meanings of education. Further, neither viewed education's primary role as the transmission of information to students: education was viewed as inherently valuable as an intellectual exploration of the soul. This position therefore provided a definition of expertise as a general set of inner ethical and knowledge-based traits that was informally and orally assessed by the instructor. In notable opposition to the "whole man" educational approach advocated by Plato and Socrates were the Sophists. The name "Sophist" itself implies the orientation: the Greek word sophia denotes skill at an applied craft, and Sophist educators focused on the development of specific applied skills for individuals studying to become lawyers or orators. Much of what we know about the Sophists anticipates today's professional or vocational training movement. Sophists were freelance teachers who charged a fee for their services and were generally in competition with one another for teaching positions. Sophists taught arete, a skill at a particular job, using a carefully prepared lecture/tutorial approach in what could be conceived as an early attempt at mass instruction. Sophist instructional methodologies were systematic, objective in nature, and made use of student feedback. It was the applied skills-building aspect of Sophism that Plato rejected, accusing the Sophists of turning education into "a marketable bag of tricks".

Sophists would likely have defined expertise as the presence of highly developed and comprehensive rhetorical and applied skills that spanned the knowledge base of the era, a definition quite distinct from the notions of Socrates or Plato. Central to Sophism was the belief that there was a single base skill - rhetoric - that once learned could be transferred to any subject. Rhetoric therefore proved to be the chief subject of Sophist instruction, the educational goal being the development of what today we might call a polymath, an individual who had mastered many subjects and whose knowledge was "complete". Sophist methods attempted to transfer rhetorical skill into all types of subject domains, including geography, logic, history, and music, through the acquisition of cognitive rules for each domain. The systematic nature of sophist instructional techniques ensured that students clearly understood learning objectives and assisted learners in gauging their own progress in achieving those objectives. This approach, then, moved educational assessment slightly more towards an objective standard than the informal, oral techniques of Socrates and Plato.

If one subscribed to the notion that education held innate worth and that its goal was the development of the "inner man" (as did Plato and Socrates), then "expertise" could be seen as the attainment of a general set of inner traits that made one wise, virtuous, and in harmony with truth. If one subscribed to the value of applied skills development (as did the Sophists), then "expertise" could be viewed as the attainment of a set of comprehensive practical abilities. Regardless of the position, the emphasis on rhetorical skills and the individualized nature of instruction in this period proscribed a generally informal assessment of expertise based on the judgment of the teacher, not strictly on objectively defined performance measures.

Much of the knowledge from the ancient school was carried through to the medieval context, but medieval institutions increasingly codified and delineated that knowledge. Subject matter was also acquiring an increasingly practical application that would serve the medieval church: geometry was required to design new church buildings, astronomy was required for calculating the dates for special observances, and Latin was required for conducting religious services and interpreting ancient texts. Latin was the central focus of nearly all education, and mastery of the language was required in order for one to be deemed "educated."

By the thirteenth century, the university had become a focal point for intellectual development, and with it came a systematized curriculum called the seven liberal arts. The curriculum was divided into an initial four-to-seven year period of study in Latin, rhetoric, and logic called the trivium (leading to the baccalaureate), followed by a second period of advanced studies in arithmetic, astronomy, geometry, and music called the quadrivium (leading to the masters or doctorate). It was by progression through these curricula that students acquired expertise and status as a master. University courses were delivered in traditional didactic manner, with the instructor presenting material that the students would assimilate, grammatically analyze, and restate to the instructor via written and oral dialogue.

Formalization of medieval educational structures also affected the amount of time required to achieve a degree. It could, for example, take up to 16 years to achieve the doctorate in theology or philosophy at the University of Paris, and as little as five percent of students ever reached this level. Most students left the system in far shorter time (usually five to ten years), taking lesser degrees that allowed them to function successfully as cathedral canons.

The medieval period saw the birth of a number of teaching techniques that were applied at the various universities, cathedral schools, and monasteries throughout Europe. It was through these techniques that learners were expected to master grammar, rhetoric, and language, all of which were the bedrock requirement for mastery of higher education, and reflected the continuing importance of communication skills carried over from the ancient context. Typical of such techniques was Scholasticism, an eleventh-century innovation greatly influenced by the questioning techniques of Abelard and later fully described by Aquinas. Scholasticism was a syllogistic learning and teaching technique that investigated apparent contradictions in ancient texts. Assessment under the Scholastic method was conducted by the master's review of student responses to such apparently contradictory source material: the student was required to apply the rules of logic in an exacting technique, with the goal of being able either to defend the "contradictory" statements as not actually containing contradiction, or to otherwise craft a convincing statement positing the human inability to resolve the contradiction (i.e., the "contradiction" was a divine truth). These interactions followed a set ritual (scholastica disputatio), whereby a master's question required from the student first a negative answer and defense, followed by a positive answer and defense, and finally a reasoned set of responses to any objections. Thus, it can be seen that the ancient topics of rhetoric and oratory still held powerful sway in the medieval curriculum.

Three primary factors characterized the development of expertise in the medieval period, all continuing to proffer the notion of teacher as expert. First, the formalization and systemization of educational structures such as the university and cathedral schools helped to strengthen and codify knowledge that could then be studied and mastered by topic. Second, the implementation of new instructional techniques, typified by the Scholastic method, moved educators away from ad hoc instruction into analyzing learning processes in a more systematic manner and establishing sequences of instruction to improve learning outcomes. Finally, the appearance of the craft guilds established a skills-based, performance-assessed, and domain-specific learning community that mastered the artisan trades under the direct guidance and supervision of experts.

One of the most significant historical events to impact education was the Industrial Revolution, a period commencing in Britain in the eighteenth century as a result of a variety of economic and technological developments. European transformation from an agrarian society into towns with seemingly innumerable factories and mills placed new demands on existing educational systems. Prior to this, education was restricted to privileged groups, including males, religious clerics, nobility, and those with the means to afford it. Even the craft guilds often charged large sums of money for admittance, restricting membership to a select pool of potential apprentices. This left education at a fundamental disconnect with the common classes, leaving them to learn what they could outside formal systems. The role of privilege and gender as it pertained to education greatly diminished with the Industrial Revolution. As a country's economic situation improved because of the new industries, the demand for supplying a continual stream of skilled industry workers forced educational structures to evolve in order to keep pace with that demand.

The postindustrial educational model therefore represents a significant shift in the development of human skill. In ancient times, learners spent time with the instructor on an individual basis, engaging in interactive dialogue and questioning. Later, in medieval times, although educational formalization was increasingly present, students still moved to the location of their master of choice, working with the master to achieve educational goals. After the industrial revolution, however, mass-production techniques from industry were applied to the educational world, employing large instructional classes and many teachers. In such an environment, the upper limit construct, the upper performance bounding of such a massed, classroom-based learning environment, began to come into play. Learners were now taught basic skills such as reading, writing, and basic math, and the goal was the development of competent industry workers.

The notion of the development of a true polymath, an educational goal tracing its roots all the way back to the ancient context (and later revived in the Renaissance in the concept of a "Renaissance man"), became increasingly disregarded in the Industrial context. Indeed, the move toward industrialization was not the only factor at play: as the amount of available knowledge exploded with the Renaissance, it became increasingly apparent that no one person would ever master in toto such a collection of knowledge. Specialization by field was now becoming the dominant paradigm when moving beyond the basic skills demanded by industry.

John Dewey was one of the early players in the attempt to apply science to education, writing a 1929 work, The Sources of a Science of Education. Much of the subsequent work in education was spearheaded by psychologists who had recently undergone the division of their field from philosophy, and the discipline of educational psychology soon came into existence. Carrying on from the pioneering work of the Wundt laboratory at Leipzig in 1879 and subsequent work by Ebbinghaus and others, learning was to be scientifically and empirically investigated as a distinct psychological process. The impact of this extraordinary shift in approach can hardly be overstated: every aspect of the learning process, including learner characteristics, instructional methodologies, psychological processes, and even physiological factors were now to be scrutinized, quantified, and aggregated into what would eventually become learning theories. This approach was also highly significant in that it threatened to remove teaching from the exclusive control of domain experts: the field of education would now seek to develop generalized scientific approaches for teaching and learning any subject, and the joint efforts of educators and psychologists would develop these approaches.

Behaviorism had posited that learners were essentially blank slates, changed by their environment and learning through the mechanisms of stimulus and response. In this view the learner was a passive recipient of knowledge, waiting for imprinting of new learning. Over time, the new stimulusresponse patterns would be strengthened and become automatic: learning was then said to have occurred. Expertise could be viewed as the development of many automatized stimulus-response patterns fully imprinted within the learner. By the mid-twentieth century, however, a number of theorists were raising questions about the ability of behaviorism to explain all learning and psychological processes. Questions surrounding the ability of learners to organize information and solve problems, for example, seemed to be left unaddressed by raw behavioral theory. This led to the development of a number of new learning theories that pointedly included mental operations as part of the description of learning. Among these were the information processing theory of Atkinson and Shiffrin and the cognitive approach of Robert M. Gagne.

Harvard University professor John B. Carroll in 1963 proposed his model of school learning. Carroll's model, although not a learning theory per se, nevertheless demonstrated a practical equation for how individual task mastery is attained and also challenged traditional notions of student aptitude. Carroll's system used five variables, three internal to the learner (amount of time required for learning the task, ability to understand instruction, and time willing to be spent on learning) and two external (time allowed for learning and quality of instruction). Carroll combined these five elements into a ratio that results in the degree of learning: degree of learning = (time actually spent on learning) / (time needed for learning). Challenging the traditional notion of student aptitude as ability, Carroll said that aptitude was more accurately a measure of learning rate, or the time an individual student requires to master a new learning task. Carroll's model depicted acquisition of expertise, therefore, as primarily a function of time: time required for learning (called aptitude), time willing to be spent on learning (called perseverance), and time allowed for learning (called opportunity).

It was Gagne's interest in school subjects that led him to conceptualize the construct of the learning hierarchy. He recognized three major relationships between initial and subsequent learning: • The learning of A was independent of the learning of B, and no sequence was implied, • The learning of A facilitated the learning of B, thus suggesting a favored sequence, and • The learning of B could not occur unless A had first been learned, thus requiring a correct sequence. These relationships are substantially incorporated into Gagne's Nine Events of Instruction. From the research literature, Gagne denned five possible learning outcomes: • Motor skills encompass the totality of the perceptual-motor domain. • Verbal information is declarative knowledge about a domain. • Intellectual skills are required to apply principles and rules to a domain. • Cognitive strategies are higher-order processes for learning and problem solving. • Attitudes are choices that a learner makes about future behavior.

Constructivists posited that students could learn only if they effectively mapped new information onto prior knowledge and experience. Stated another way, learners were said to construct their own knowledge, which may or may not map to what others consider objective reality... The design of constructivist learning environments in schools can be a significant step forward. Early research indicates that students can greatly improve their knowledge acquisition skills using technologies and constructs based on information processing... Sometimes the difference in learning requirements is presented as a conflict between "instructivist" perspectives and "constructivist" perspectives. Our view is that both conceptualizations are useful, depending on the kinds and stages of learning that must be accomplished...Conversely, if an objective of education is to prepare students for future lifelong self-directed learning, then constructivist learning environments appear to be far more promising than the standard classroom instruction. Stated another way, one instructional approach does not fit every learning situation.

Spiro, Feltovich, Jacobson, and Coulson have focused research on the deficiencies of past educational techniques and made recommendations for adjustments in instructional design to improve educational outcomes and preparation for continued learning. These researchers have made a case that real-world situations are much more complex and illstructured than most instructional systems reflect, and that these underlying biases and assumptions in the design of instruction lead to poor learning. Spiro and colleagues recommend a constructivist learning environment that emphasizes the real world complexity and ill-structured nature of many areas of learning.

K. Anders Ericsson authored a salient line of empirical research investigating expert performance, a term he used to describe consistent, measurable, and reproducible performance of the world's premier performers in a wide variety of domains. Ericsson's model of expert performance differentiated from earlier expertise models such as Fitts and Posner and Chi and Glaser in its proposition that time and/or practice alone could not produce the highest levels of human performance. Ericsson proposed that a particular type of exercise that he termed deliberate practice, a technique involving a learner's full mental engagement and oriented on the goal of overcoming current performance boundaries, is required for such achievement. Further developing the model, Ericsson and Delaney provided an expanded description on the specialized techniques expert performers employ for both circumventing the limitations of short-term memory and rapidly accessing long-term memory. This line of research has investigated viability of the expert performance model across a wide variety of performance domains, including memory, sports, chess, and music. Ericsson's model, with its emphasis on objective and verifiable assessment of skill levels, remains a leading empirical explanation of the acquisition of expert performance in a wide variety of performance domains.

Tacit Knowledge, Practical Intelligence, and Expertise, A. Cianciolo, R. Sternberg

The drive to excel has long challenged humans to push their bodies, minds, and technologies in the determined pursuit of success. People have demonstrated their devotion to excellence through the years of effort and practice they have been willing to invest in accomplishing their goals. For example, Simon and Chase observed that no one had ever attained the rank of Grandmaster in chess without at least a decade of intense preparation. This observation has since been extended to many domains, including music, sports, and academia. Despite folk tales about extraordinary performances by very young individuals, it is clear that the most eminent individuals in any field do not exhibit expert levels of performance prior to an extended period of preparation.

One of the enduring debates over many years of study is whether the development of expertise is largely attributable to unusual characteristics of individuals, often thought of in terms of largely inherited talents, or of their learning histories. Because expertise is acquired over many years, perhaps as a result of more intense, sustained, and programmatic application of the identical mechanisms that underlie average levels of attainment, the study of expert performance is directly relevant to the study of typical human development.

Our research has been devoted, in part, to creating a better understanding of the cognitive mechanisms that allow people to develop and use the practical intellectual abilities required for success in everyday life. As such, our work represents a link between the study of typical human development and the exploration of expertise. Of particular interest to us is the way in which people use their intellectual capabilities to adapt to and succeed in particular environments. Expertise, whether demonstrated in such everyday feats as reading and writing, or in the exceptional accomplishments of artists, athletes, and scholars, reflects the outcome of people's active engagement in the world around them.

We briefly outline our conceptualization of expertise; then we describe the fundamental role that practical intelligence and tacit knowledge are theorized to play in expert performance. We then describe the scientific exploration of practical intelligence and tacit knowledge - their nature, measurement, and relation to expertise. Finally, we discuss a variety of approaches used to enhance practical intelligence and tacit knowledge and suggest some directions for future research.

Of particular interest to us is the way in which people use their intellectual capabilities to adapt to and succeed in particular environments. Expertise, whether demonstrated in such everyday feats as reading and writing, or in the exceptional accomplishments of artists, athletes, and scholars, reflects the outcome of people's active engagement in the world around them. In this chapter, we discuss a psychological approach to exploring expertise that is based on the theory of practical intelligence and tacit knowledge. This approach represents an attempt to explain the cognitive mechanisms underlying the human ability to adapt to, select, and shape environments in the pursuit of personally valued goals and success in life. We briefly outline our conceptualization of expertise; then we describe the fundamental role that practical intelligence and tacit knowledge are theorized to play in expert performance. We then describe the scientific exploration of practical intelligence and tacit knowledge - their nature, measurement, and relation to expertise. Finally, we discuss a variety of approaches used to enhance practical intelligence and tacit knowledge and suggest some directions for future research.

The most common psychological approach to defining expertise is to rely on an empirical definition based on individual differences. That is, an expert is defined as someone whose level of performance exceeds that of most others.' For example, Ericsson and Smith observed that some individuals stand apart from the majority. These scholars view the central goal of the study of expertise as finding out what distinguishes these outstanding individuals from the less outstanding in some domain of activity...Among the characteristics explored are general information-processing capabilities, such as strategizing and problem solving, the nature, quantity, and organization of expert knowledge, and, more recently, cognitive complexity.

Another perspective on expertise, the triarchic perspective, takes a broader, developmental approach, and posits that success in life is determined by one's analytical, creative, and practical abilities, which improve with practice and experience. The value of the triarchic perspective to the broader, psychological study of expertise is that it provides an opportunity to rethink fundamental issues including what is an appropriate definition of expertise.

The prototype view of expertise maintains that expertise is relatively domain specific and that the attributes of experts may be specific to a time and place, Chapter 4. This view maintains the importance of domain-general information-processing capabilities, such as problem solving, while recognizing that expertise and its requisite knowledge, skills, and abilities are defined quite differently, depending on the environment in which people develop and express their expertise. Importantly, the prototype view of expertise recognizes the diversity of skills that can lead to successful performance, and that expertise can be thought to exist in degrees rather than in an all-or-none fashion.

The theory of practical intelligence and tacit knowledge explicitly addresses the interchange between information-processing capability and experience in particular environmental contexts, making it an important source of insight into expertise. Specifically, the theory posits that the development of practically intelligent behavior, a critical aspect of success in everyday life, occurs through a cycle of inquiry, knowing, and action, that is, a cycle of engaging the environment, acquiring tacit knowledge, and performing in a practically intelligent manner.

The word "tacit" is used to characterize exchanges that are carried out without the use of words or speech, and to describe shared arrangements that have arisen without explicit agreement or discussion. Tacit knowing therefore represents a person-environment exchange that is not articulated and that arises without explicit attempt to link environmental stimulation to phenomenological experience. Although the idea that people's actions are subject to unconscious influences dates back to Sigmund Freud in the late 1800s, scientist and philosopher of science Michael Polanyi was among the first to discuss formally the concept of tacit knowledge, noting its influence on perception and scientific thinking. Specifically, Polanyi argued that "we can know more than we can tell" and that tacit knowledge underlies a wide range of skills, from tool use to application of the scientific method.

Wagner and Sternberg defined tacit knowledge as "knowledge that usually is not openly expressed or stated... is not directly taught or spoken about, in contrast to knowledge directly taught in classrooms", with the qualification that "we do not wish to imply that this knowledge is inaccessible to conscious awareness, unspeakable, or unteachable, but merely that it is not taught directly to most of us". Wagner and Sternberg have presented tacit knowledge as an enabler of practically intelligent behavior, which, in turn, is believed to be a critical aspect of expertise.

Practical intelligence is defined as the ability to acquire tacit knowledge from everyday experience and to apply this knowledge to handling everyday practical problems in which the information necessary to determine a solution strategy is often incomplete. Practical intelligence is a component of Sternberg's wideranging triarchic theory of successful intelligence, which posits three distinct aspects of human intelligence: analytical, creative, and practical.

Sternberg describes the acquisition of tacit knowledge and consequent enhancement of practical intelligence as driven by knowledge-acquisition components. Knowledge-acquisition components characterize the executive cognitive processes involved in the often unconscious manipulation of information found in novel situations in order to learn from experience. These three cognitive processes are (a) selective encoding, (b) selective combination, and (c) selective comparison. Selective encoding is the selection of information from the environment that is relevant to understanding the current situation or to solving the problem at hand. Selective combination is the integration of multiple pieces of selectively encoded information into a unified whole that creates a meaningful pattern and, eventually, a knowledge structure. Selective comparison is the comparison of newly formed patterns of information or knowledge structures to previously formed knowledge structures. Accurate selective encoding, selective combination, and selective comparison results in an increased body of tacit knowledge and, consequently, more practically intelligent behavior.

Although the exact nature of general intelligence is yet unknown, it is commonly defined as the highly general capability to process information and is believed to have specific neurological substrates. To the extent that neurological functioning undergirds all mental activity, practical intelligence should show some relation to general intelligence. Practical intelligence is theoretically distinct from general intelligence, however, in that general intelligence is viewed as a relatively stable characteristic of individuals, whereas practical intelligence is viewed as developing with effort and experience. Moreover, the development of practical intelligence - through the acquisition of tacit knowledge - occurs via an interaction between an individual's existing level of competency and an environmental context. One's level of general intelligence is believed to exist largely independently of one's knowledge and experience.

Crystallized intelligence has been defined as the outcome of "experiential-educativeacculturation influences" on one's biological capacity. Tests of crystallized intelligence commonly assess vocabulary, reading comprehension, and other verbal skills. Practical intelligence resembles crystallized intelligence through their shared dependence on experience and similar developmental aspects. In contrast to crystallized intelligence, however, practical intelligence is applied to identifying and solving problems that often do not have one correct solution strategy or clearly right answer.

In contrast to declarative knowledge of facts and concepts, procedural knowledge is knowledge of how to execute some task. Procedural knowledge typically is viewed as the end state of a learning process for tasks that can be automatized with practice, such as typing and other psychomotor skills. Like procedural knowledge, tacit knowledge is action oriented, gained from experience, applied unconsciously, and often difficult to verbalize. However, tacit knowledge is not viewed as an automatic response produced from repeated exposures to the same patterns of stimuli. Rather, it is viewed as an adaptive intellectual resource stemming from the active interaction between individuals and their dynamic environment.

The general results from exploring the constructs of practical intelligence, tacit knowledge, and their measurement have indicated that practical intelligence does not overlap substantially with general intelligence, crystallized intelligence, or personality. Importantly, the cause for this lack of overlap does not appear to be differences in the amount of domain-specific knowledge featured on the assessments of each construct; tacit knowledge also does not overlap substantially with technical job knowledge. Practical intelligence and tacit knowledge do show a noteworthy relation to everyday expertise in varied settings and is revealed using diverse performance criteria.

In research conducted by multiple scholars, tacit knowledge has shown a notable relationship to many diverse demonstrations of expertise. That is, individuals scoring better on measures of tacit knowledge (usually tacit-knowledge inventories) have tended to show higher levels of performance, as measured by various criteria, and vice versa.

Wagner and Sternberg have noted two ways in which one's body of tacit knowledge can be enhanced: (1] making tacit knowledge explicit and sharing it, and (2] improving people's ability to engage their environments and learn from experience. Substantial research and program development have also been devoted to improving people's practical problem-solving skills, some of which has been conducted by Sternberg and his colleagues. We summarize below these diverse research and development efforts.

Methods to make tacit knowledge explicit are at the heart of a number of accepted practices recognized for their potential benefit to personal and professional development. These practices include psychotherapy, which involves uncovering tacit knowledge that may be maladaptive, and mentoring, which involves the articulation of why a particular action should be taken at a particular time. Although some may reject the notion that tacit knowledge can be made explicit, its potential to contribute to the development of expertise has been explored and advocated by a number of scholars from a variety of theoretical perspectives. The central belief shared by these scholars, and others, is that because most of the relevant know-how that distinguishes different levels of expertise is acquired through experience, methods that stimulate the process of thinking about what one is doing and why, and talking about it with others, will facilitate the development of expertise.

Communities of practice, defined as groups of people who informally come together to exchange knowledge and experience in a shared domain of interest, have been increasingly recognized as an effective mechanism to develop expertise through sharing tacit knowledge. They are distinguished from workgroups and teams in that the nature of membership is selfselection versus assignment by an organizational authority, and the purpose of membership is to develop capability, and build on and exchange knowledge rather than accomplish a more specific task or assignment.

Facilitating tacit-knowledge acquisition is a more indirect approach to enhancing one's body of tacit knowledge than is sharing explicit tacit knowledge. However, this indirect approach can be expected to have more lasting effects on one's practical intelligence. Explicit tacit knowledge, shared in communities of practice, eventually becomes outdated, sometimes very rapidly, as the mores of cultures shift (e.g., by becoming multiethnic] or as the operational environment changes (e.g., by introducing new technological capability). Learning how to acquire tacit knowledge, however, never becomes outdated.

Approaches to facilitating tacit-knowledge acquisition target the three cognitive processes thought to underlie knowledgeacquisition: selective encoding, selective combination, and selective comparison. Specifically, instruction is designed to draw students' attention to how the relevant information in the environment or from previous experience can be selected to guide decision making and problem solving, how relevant information can be combined to form patterns meaningful to understanding the problem at hand, and how the knowledge acquired from past experience can be compared to new knowledge to inform decisions and action. It is believed that as students reflect on how they are using information from the environment and from experience to solve problems, they will come to value their experiences as opportunities for learning.

The philosopher John Dewey believed that reflective thought - the critical analysis of one's ideas and behaviors - was an important aspect of good thinking skills and effective problem solving. Dewey's work has influenced the thinking of numerous philosophers and psychologists who have sought to understand and enhance problem-solving and experiencebased learning. These scholars have used a wide range of methods to facilitate inquisitiveness and experience-based learning - from using stories to engage children in the philosophical analysis of problems to training the particular cognitive processes involved in insight and learning from context to exploring complex problems by discussing multiple points of view.

Identifying experts' tacit knowledge using performance modeling also offers an alternative to relying on traditional methods for eliciting tacit knowledge. To date, the elicitation of tacit knowledge has relied on the verbalized recollections of experts, which provide unreliable information regarding the actual conditions (or environmental cues) that triggered particular actions. Moreover, mathematical modeling of tacit knowledge may provide some insight into what specifically is learned when tacit knowledge is acquired, thus making it easier to make tacit knowledge explicit or to facilitate tacit-knowledge acquisition.

The Influence of Experience and Deliberate Practice on the Development of Superior Expert Performance, K. Ericsson

There are several factors that influence the level of professional achievement. First and foremost, extensive experience of activities in a domain is necessary to reach very high levels of performance. Extensive experience in a domain does not, however, invariably lead to expert levels of achievement. When individuals are first introduced to a professional domain after completing their basic training and formal education, they often work as apprentices and are supervised by more-experienced professionals as they accomplish their work-related responsibilities. After months of experience, they typically attain an acceptable level of proficiency, and with longer experience, often years, they are able to work as independent professionals. At that time most professionals reach a stable, average level of performance, and then they maintain this pedestrian level for the rest of their careers. In contrast, some continue to improve and eventually reach the highest levels of professional mastery.

More recently, researchers of expert performance have found that there are many types of experience and that these different types have qualitatively and quantitatively different effects on the continued acquisition and maintenance of an individual's performance. This framework proposes that some types of experience, such as merely executing proficiently during routine work, may not lead to further improvement, and that further improvements depend on deliberate efforts to change particular aspects of performance.

The general view is that the individual's potential is limited by innate biological capacities that will ultimately constrain the highest level of achievement. Sir Francis Galton is often recognized for articulating this view in the igth century. His pioneering book, Hereditary Genius, presented evidence that height and body size were determined genetically. Most importantly, he argued that innate mechanisms also regulated size and characteristics of internal organs, such as the nervous system and the brain, and thus must similarly determine mental capacities. Galton clearly acknowledged the need for training and practice to reach high levels of performance in any domain. However, he argued that improvements of performance for mature adults are rapid only in the beginning of training and that subsequent increases diminish, until "Maximal performance becomes a rigidly determinate quantity". According to Galton, the relevant heritable capacities determine the upper bound for the performance that an individual can attain through practice, and reflect the immutable limit that "Nature has rendered him capable of performing". According to Galton, the characteristics that limit maximal performance after all benefits of training have been gained must, therefore, be innately endowed. Carton's arguments for the importance of innate factors for attaining the highest levels of performance were compelling and, thus, have had a lasting impact on our culture's view of ability and expertise.

Simon and Chase proposed that future experts gradually acquired patterns and knowledge about how to react in situations by storing memories of their past actions in similar situations. Hence, performance is assumed to improve as a consequence of continued experience...Some scientists started to consider the possibility that expertise was an automatic consequence of lengthy experience, and they considered individuals with over ten years of full-time engagement in a domain to be experts. These scientists typically viewed expertise as an orderly progression from novice to intermediate and to expert, where the primary factors mediating the progression through these stages were instruction, training, and experience. Thus, the primary criteria for identifying experts were social reputation, completed education, accumulated accessible knowledge, and length of experience in a domain (over ten years)... Several reviews over the past decade, however, have raised issues about this characterization of expertise. Most importantly, when individuals, based on their extensive experience and reputation, are nominated by their peers as experts, their actual performance is occasionally found to be unexceptional.

Once it is clear that social and simple experience-based indicators of expertise do not guarantee superior performance, an alternative approach is required. Ericsson and Smith proposed that the focus should not be on socially recognized experts, but rather on individuals who exhibit reproducibly superior performance on representative, authentic tasks in their field. For example, the focus should be on physicians who can diagnose and treat patients in a superior manner, on chess players who can consistently select the best moves for chess positions, and on athletes and musicians who exhibit superior performance in competitions. The first step in a science of expert performance requires that scientists be able to capture, with standardized tests, the reproducibly superior performance of some individuals, and then be able to examine this performance with laboratory methods, as will be described in the next sections.

The most compelling evidence for the role of vast experience in expertise comes from investigators who have shown that, even for the most talented individuals, ten years of experience in a domain (ten-year rule) is necessary to become an expert and to win at an international level. Subsequent reviews have shown that these findings extend to international-level success in music composition, as well as to sports, science, and the arts. A closer examination of the evidence for the ten-year rule shows that the number ten is not magical. In fact, the number of years of intense training required to become an internationally acclaimed performer differs across domains. For example, elite musicians (disregarding the biased standards for child prodigies) need closer to 20 to 30 years of training and often peak when they are around 30 to 40 years old. Further, outstanding scientists and authors normally published their first work at around age 25, and their best work follows around ten years later.

In virtually every aspect of human activity there have been increases in the efficiency and level of performance. Over centuries and millennia, across domains of expertise, people have developed methods for accumulating and preserving discovered knowledge and skills and produced tools and refined their technique of application. Hence, they have assembled a body of organized knowledge that can be transferred from the current to the next generation through instruction and education. It is no longer necessary for individuals to discover the relevant knowledge and methods by themselves. Today's experts can rapidly acquire the knowledge originally discovered by the pioneers.

More generally, record-breaking levels of performance are nearly always originally attained by only a single eminent performer. However, after some time, other athletes are able to design training methods that allow them to attain that same level of performance. Eventually, these training methods become part of regular instruction, and all elite performers in the domain are expected to attain the new higher standard.

At the same time the best training environments are not sufficient to produce the very best performers, and there are substantial individual differences even among individuals in these environments. Can differences in the amount and type of domainrelated activities that individuals engage in explain individual differences in music performance, even among the best performers?

The core assumption of deliberate practice is that expert performance is acquired gradually and that effective improvement of performance requires the opportunity to find suitable training tasks that the performer can master sequentially - typically the design of training tasks and monitoring of the attained performance is done by a teacher or a coach. Deliberate practice presents performers with tasks that are initially outside their current realm of reliable performance, yet can be mastered within hours of practice by concentrating on critical aspects and by gradually refining performance through repetitions after feedback. Hence, the requirement for concentration sets deliberate practice apart from both mindless, routine performance and playful engagement, as the latter two types of activities would, if anything, merely strengthen the current mediating cognitive mechanisms, rather than modify them to allow increases in the level of performance.

Longitudinal studies of elite performers have found that the most potent variables linked to performance and future improvements of performance involved parental support, acquired task-specific (in this case, tennis) skills, and motivational factors including concentration. Similarly in chess, Charness and his colleagues found that the amount of solitary chess study was the best predictor of chess skill, and when this factor was statistically controlled, there was only a very small benefit from the number of games played in chess tournaments.

In direct contrast to the acquisition of everyday skills, expert performers continue to improve their performance with more experience as long as it is coupled with deliberate practice. The key challenge for aspiring expert performers is to avoid the arrested development associated with automaticity and to acquire cognitive skills to support their continued learning and improvement. By actively seeking out demanding tasks - often provided by their teachers and coaches - that force the performers to engage in problem solving and to stretch their performance, the expert performers overcome the detrimental effects of automaticity and actively acquire and refine cognitive mechanisms to support continued learning and improvement. The expert performers and their teachers identify specific goals for improving particular aspects of performance and design training activities that allow the performer to gradually refine performance with feedback and opportunities for repetition (deliberate practice). The performers will gradually acquire mechanisms that increase their ability to control, self-monitor, and evaluate their performance in representative situations from the domain and thus gain independence from the feedback of their teachers. Although the overall structure of these mechanisms reflects general principles, the detailed structure and practice activities that mediate their acquisition will reflect the demands of that particular activity and thus differ from one domain of expertise to another.

The theoretical framework of deliberate practice asserts that improvement in performance of aspiring experts does not happen automatically or casually as a function of further experience. Improvements are caused by changes in cognitive mechanisms mediating how the brain and nervous system control performance and in the degree of adaptation of physiological systems of the body. The principal challenge to attaining expert level performance is to induce stable specific changes that allow the performance to be incrementally improved.

Research on deliberate practice in music and sports shows that continued attempts for mastery require that the performer always try, by stretching performance beyond its current capabilities, to correct some specific weakness, while preserving other successful aspects of function. This type of deliberate practice requires full attention and concentration, but even with that extreme effort, some kind of failure is likely to arise, and gradual improvements with corrections and repetitions are necessary.

The perspective of deliberate practice attributes the rarity of excellence to the scarcity of optimal training environments and to the years required to develop the complex mediating mechanisms that support expertise. Even children considered to have innate gifts need to attain their superior performance gradually, by engaging in extended amounts of designed deliberate practice over many years. Until most individuals recognize that sustained training and effort is a prerequisite for reaching expert levels of performance, they will continue to misattribute lesser achievement to the lack of natural gifts, and will thus fail to reach their own potential

Elite performers in many diverse domains have been found to practice, on the average, roughly the same amount every day, including weekends, and the amount of practice never consistently exceeds five hours per day. The limit of four to five hours of daily deliberate practice or similarly demanding activities holds true for a wide range of elite performers in different domains, such as writing by famous authors, as does their increased tendency to take recuperative naps. Furthermore, unless the daily levels of practice are restricted, such that subsequent rest and nighttime sleep allow the individuals to restore their equilibrium, individuals often encounter overtraining injuries and, eventually, incapacitating "burnout."

Defining and Describing Reason, J. Leighton

Reasoning has, on the one hand, been defined narrowly as the process of drawing deductive inferences and, on the other hand, as an aspect of thinking that is involved not only in drawing inferences but in making decisions and solving problems as well. Has reasoning been defined so broadly and redefined so frequently that it has lost its significance? Put another way, could reasoning be legitimately subsumed under problem solving or decision making without any loss? I no longer think so.

In the present book, reasoning is broadly defined as the process of drawing conclusions. Moreover, these conclusions inform problem-solving and decision-making endeavors because human beings are goal driven, and the conclusions they draw are ultimately drawn to help them serve and meet their goals.

A prominent theme in the book is that of reasoning as mediator. If we wanted to personify reasoning, it would take on the character of a middleman or middlewoman in a company or enterprise. As a middleman, reasoning works behind the scenes, coordinating ideas, premises, or beliefs in the pursuit of conclusions. These conclusions may sometimes find their way to the surface in the form of observable behavior as when someone exclaims "I have an idea!" or argues "I think your idea is not going to work because—" Other times, the conclusions do not find their way to the surface but, rather, stay beneath the surface and function internally as antecedent conditions that feed into chains of productions for problem solving... In either case, whether conclusions become externally observable or stay beneath the surface to help to initiate problem-solving endeavors, reasoning processes are at work. Unfortunately, these processes may not often be acclaimed because they work behind the scenes and in the shadow of more observable functions such as problem solving and decision making. Despite their covert nature, however, understanding how reasoning processes function is imperative to maximizing our efforts at solving problems and making decisions.

Drawing true conclusions facilitates problem solving. True conclusions facilitate problem solving because they are reliable representations of the external environment. Therefore, true conclusions increase the likelihood that a problem's features are being depicted faithfully so that the best strategy for solving the problem can be selected.

The difficulty of verifying a conclusion's truth does not mean that we are doomed to a life of false conclusions. In the absence of being able to verify a conclusion directly, we can evaluate how our premises (or beliefs) entail the conclusion of interest. In other words, we can learn to scrutinize our claims to truth. Our claims to truth are the processes by which we generate conclusions. Do we generate conclusions that follow necessarily from a given set of premises? Or only very likely from a given set of premises? In the end, we may not be able to control our ability to directly verify a conclusion's truth, but we may be able to control the cohesion or soundness of the reasoning that lead up to it.

Conclusions are commonly described as being generated either deductively or inductively. For example, a conclusion that is derived deductively from a set of premises follows necessarily from its premises; that is, the premises provide conclusive grounds for the conclusion. Moreover, if the conclusion is derived deductively from true premises, then the conclusion is necessarily true. This is one way to yield true conclusions without checking them against reality: If the premises are true, then the conclusion drawn must be true. Conclusions derived deductively are considered necessary because they contain the same amount of information as that found in the premises leading up to it; necessary conclusions represent information that is already implicitly contained in the premises.

In contrast, a conclusion that is derived inductively from a set of premises does not follow necessarily from its premises, although it might be strongly supported by them. A conclusion that is derived inductively from true premises is likely to be true but it is still not necessarily true. Conclusions derived inductively are considered unnecessary because they contain more information than that found in the premises leading up to it. Unnecessary conclusions represent information that goes beyond the information already contained in the premises. Although the truth of necessary or unnecessary conclusions must be checked against reality (except when reasoning deductively from true premises), knowing a conclusion's necessity is still informative because it indicates the cohesion of the reasoning that underlies it.

The advantage of problem solving is that its outcome can be judged right or wrong, unequivocally, by determining how well it resolves the problem in the first place. In contrast, the outcome of reasoning is not so unequivocally judged because reasoning does not yield a solution but, rather, a conclusion; a conclusion whose origin is not from a problem but from a set of beliefs. To judge a conclusion, then, one must know how it was generated and the truth of the beliefs leading up to it. The standard for judging a conclusion depends on different principles. As mentioned previously, a conclusion can be judged according to its necessity and according to its truth.

Although we do not normally think about how fundamental reasoning is to our well-being, reasoning is like breathing to the mind. We are constantly doing it but we rarely take notice of it. If it fails, however, we are paralyzed. Imagine being unable to infer conclusions from a conversation? Or being unable to reach a solution to an important life problem? We reason when we learn, criticize, analyze, judge, infer, evaluate, optimize, apply, discover, imagine, devise, and create - and the list goes on because we draw conclusions during so many of our daily activities. Given that reasoning underlies so many of our intellectual activities, how do we operate, apply, and nurture our reasoning?

Teaching Reasoning, R. Nickerson

As used in the psychological literature, reasoning has a variety of connotations that differ in their inclusiveness. At one extreme, the term is used to connote what once was called ratiocination, the process of deductive inferencing. At the other, it encompasses many aspects of thinking, in addition to deduction, that are involved in drawing conclusions, making choices, solving problems, and trying to figure out what to believe. Researchers and educators who have written about the teaching of reasoning have, I believe, had relatively inclusive connotations of reasoning in mind when doing so, and it is reasoning in a broad sense that is of interest here.

Among many distinctions that have been made regarding reasoning by philosophers and psychologists, perhaps none is more basic than the distinction between deduction and induction. Deduction involves making explicit in conclusions what is contained by implication in the premises of an argument; induction, in contrast, involves going beyond what is implicitly contained in the evidence from which conclusions are drawn. Polya, whose distinction between demonstrative and plausible reasoning is essentially the same as the distinction between deduction and induction, characterizes the distinction as the difference between reasoning that is "safe, beyond controversy, and final" and that that is "hazardous, controversial, and provisional."

Deduction is readily formalized; induction is not. Widely accepted standards are available for evaluating the quality of deductive reasoning; how to evaluate inductive reasoning is a matter of considerable debate. Whitehead's reference to the theory of induction as "the despair of philosophy" reflects the frustration that scholars have experienced in trying to codify inductive reasoning; but recognition of the importance of this type of reasoning is seen in Polya's observation that "in dealing with problems of any kind, we need inductive reasoning of some kind".

Most of the challenges to reasoning that life presents are not solvable simply by a series of deductions from the information given. Most real-life problems do not come with all the information that is essential to their solution; typically one must do some searching for information to fill in what is missing, or to resolve ambiguities, just to make a decent start. Even when one has obtained all the information that can reasonably be obtained, it is likely to be impossible to organize the situation so that the solution will be the final conclusion of a neat deductive chain. There is likely to be a need to make some assumptions, to engage in probabilistic thinking, and to settle for conclusions that are less than certain. This is what it means to reason inductively.

I want to make a distinction that is related to that between deductive and inductive reasoning, but is not the same. This is the distinction between reasoning as a process of coming to conclusions and reasoning as justification of conclusions. Both involve deduction and induction. The first tends to be informal and to include conjectures, false starts and often much "churning." The second tends to be more formal and terse, and expressed as carefully developed argumentation. The first is what one does when trying to decide what to believe on some subject. The second is what one does when one explains, as clearly and concisely as one can, why one has come to a particular conclusion on the matter: "I have concluded X and here is my reasoning."..For present purposes, I prefer the terms exploratory reasoning and justificatory reasoning to connote the distinction I have in mind. Exploratory reasoning is reasoning that goes into the development and refinement of an argument; justificatory reasoning is the argument in its final form.

Just as it is easier to judge the validity of mathematical proofs than to judge the quality of the reasoning that went into their construction, because there are widely accepted criteria for doing the former but not for doing the latter, so it is easier to judge the quality of reasoning as the explication of reasons for believing a conclusion to be true than to judge the quality of the reasoning that went into the arrival at the conclusion initially.

For purposes of this chapter, reasoning is taken to include both deduction and induction and both exploratory and justificatory reasoning, as distinguished above. It involves the making of inferences or the drawing of conclusions, as well as such closely related cognitive activities as searching for and weighing evidence, analyzing implications, constructing and evaluating arguments and counterarguments, identifying missing assumptions, judging plausibility, establishing and evaluating beliefs, and diagnosing situations. It is implicated in problem solving, decision making, goal evaluation, and other cognitively demanding activities that are critically important to intelligent behavior.

What I mean by good reasoning in this chapter is reasoning that leads to the drawing of justified conclusions and their explication; poor reasoning, in contrast, is reasoning that leads to the drawing of conclusions that are not justified. This conceptualization begs the question of what it means for a conclusion to be justified - justified in the eyes of whom? Equating justification with being well supported by evidence does not help a lot, because evidence also is a matter of interpretation to some degree. But discussion of such difficulties is beyond the scope of this chapter. I shall assume a sufficient consensus regarding the difference between justified and unjustified conclusions for present purposes.

Does good reasoning in science differ from good reasoning in the humanities, or history, or law, or theology? Does the diagnosis of an illness require a qualitatively different type of reasoning than the diagnosis of an automotive problem? I want to argue that there are many qualities, abilities, and propensities that are supportive of good reasoning independently of who does it or the subject on which it is focused. They do not guarantee that one will reason well, but they increase the likelihood.

Abilities, Qualities and Propensities that Good Reasoners are Likely to Possess: • Intelligence • Domain-specific knowledge • General knowledge about human cognition • Knowledge of common limitations, foibles, pitfalls • Self knowledge • Knowledge of tools of thought • Ability to analyze and evaluate arguments • Good judgment • Ability to estimate • Sensitivity to missing information • Ability to deal effectively with uncertainty • Ability to take alternative perspectives • Ability to reason counterfactually • Ability to manage own reasoning • Reflectiveness • Curiosity, inquisitiveness • Strong desire to hold true beliefs • Willingness to work at reasoning

What should the specific objectives of efforts to teach reasoning be? The obvious answer is to help students develop the abilities, qualities and propensities that we associate with good reasoning and avoid or compensate for impediments to the same. Some of these things are undoubtedly easier to develop than others, and there are likely to be differences among students with respect to their potential to acquire them. How much emphasis is merited by each of the abilities, qualities, and propensities mentioned probably depends on the existing characteristics of the students and teachers involved and on a number of situational variables, but all of them deserve consideration, and improvement with respect to any of them should translate into better reasoning.

There can be little doubt that intelligence, as measured by conventional IQ tests, is a reasonably good predictor of success both in academic performance and in the world of work. Other things equal, high intelligence is an asset for good reasoning. For people interested in the possibility of improving reasoning ability the question naturally arises as to whether intelligence can be increased by training. This is an old question, and one that is still being debated. The debate is clouded, however, by issues of definition. To the extent that intelligence is equated with Spearman's g, the prevailing opinion appears to be that training is unlikely to increase it very much. Although there are reasons to believe that at least modest gains are possible. If one takes a broad view of what constitutes intelligence, as several theorists do, the possibility of increasing it substantially in one or more respects is generally seen to be feasible.

Perkins, who distinguishes three dimensions of intelligence - neural, experiential, and reflective - argues that both experiential intelligence ("the contribution of a storehouse of personal experience in diverse situations to intelligent behavior") and reflective intelligence ("the contribution of knowledge, understanding, and attitudes about how to use our minds to intelligent behavior") are learnable, and only neural intelligence is not. "Without question, two of the three dimensions of intelligence can be advanced by learning - experiential intelligence through in-depth experiences and reflective intelligence through the cultivation of strategies, attitudes, and metacognition". Perkins sees a focus on reflective intelligence - "the control system for experiential and neural intelligence" - as providing the best opportunity for improving people's reasoning.

A caveat: Although high intelligence is an asset for good reasoning, it is not a guarantee of it. It does not, for example, ensure that those who have it will be immune to the foibles, such as a my-side bias in argument production that afflict less gifted mortals. More generally, high intelligence does not ensure that those who have it will hold only well-justified beliefs. The debate regarding the teachability of intelligence is likely to continue. However that debate progresses, if intelligence, however defined, is teachable, teaching it is a commendable goal, but not enough by itself to ensure better reasoning broadly conceived.

Some researchers believe that reasoning ability is relatively domain specific; others believe that good reasoning is the same independently of the domain in which it occurs. One question regarding the possibility of improving reasoning through training that has evoked much discussion is that of whether it is better to try to teach principles and strategies of reasoning in a domain-independent way, with the expectation that what is learned will be applicable across domains, or to teach reasoning within domains - how to reason about mathematics, how to reason about history, law, automotive mechanics, and so on. Regardless of what one considers the answer to this question to be, it is obvious that one cannot reason very deeply about a subject unless one has some knowledge of that subject, and no one, so far as I know, contends otherwise. So, if one wishes to reason well about a particular subject, one needs to learn what one can about that subject.

The following distinctions and ideas seem fundamental to good reasoning.

• The difference between reasoning and case building. One is reasoning when one impartially considers evidence and attempts to determine what conclusion(s) it justifies. One is case building when one attempts to marshal evidence to support a conclusion while ignoring or discounting evidence that tells against it. Case building is what one does when one engages in a debate with the goal of winning, whether or not one believes the proposition one is committed to defend.

• The difference between reasoning and rationalizing. There is a great difference between impartially looking for evidence to determine what one should believe or do and attempting to put an existing belief or something one has done in the best possible light. We appear to be quite good at coming up with reasons for decisions we have made, after having made them, but it is often doubtful that those reasons were instrumental in the actual decision process. The tendency to rationalize is easy to understand; no one wants to admit that one holds beliefs that are unfounded or makes decisions that do not have a rational basis. But unawareness of the difference between reasoning and rationalizing, and of the propensity we all have to rationalize, can only compound the problem.

• Overly simple causal explanations. It appears that our minds, as Gabor has argued, cannot tolerate a vacuum; they find an explanation for everything. Moreover, the tendency is to account for events in terms of simple, often single-factor, causes. What caused the American Revolution? Taxation without representation. Why is Mr. X so stingy? Because he grew up during the Great Depression. Such explanations rest on the assumption that events typically have simple, single-factor causes. Reflection makes it clear that this assumption must be wrong and that what are, at best, contributing factors are often mistaken for sufficient causes.

• Emotional factors. Can anyone doubt that emotions affect reasoning? Heated disputes are seldom won by reason. Typically when two people are engaged in one, each is motivated to marshal as much support as possible for the position he or she is defending, and to give as little credence as possible to anything said or unsaid that weighs against it. The more emotional the confrontation, the less motivated the parties are likely to be to treat evidence objectively.

Research has revealed a variety of limitations of human reasoning and many ways in which it often goes wrong. Some knowledge of common difficulties, biases, and foibles should be useful in helping one both to recognize them when one encounters them and, perhaps, to avoid displaying them oneself. People should know about such documented human tendencies as those of giving more credence to claims that one likes than to those one dislikes, of seeking evidence to confirm favored hypotheses while ignoring or discounting evidence that would tell against them, of finding it easier to believe what one prefers to believe, of generally being overconfident of the accuracy of one's own judgments, of misjudging the extent to which one could anticipate events before they occurred (hindsight bias), of overestimating the size of one's own contribution to a group effort relative to the contributions of other members of the group, of overestimating the degree to which other people's knowledge, beliefs, and behavior are similar to one's own.

In addition to knowing about cognition in general, an individual should benefit from knowing something of his or her own particular strengths and limitations that relate to reasoning. The realization that one has a tendency to jump to conclusions without giving adequate attention to available evidence, or that one characteristically fails to consider arguments that could be brought against positions one holds, or that one typically accepts claims that one reads without making an attempt to assess their plausibility, could be a point of departure for an effort to improve one's reasoning in specific respects.

By tools of thought I mean to include both formal systems (logic and mathematics) that have been developed to facilitate deductive reasoning and informal strategies or heuristics (rules-of-thumb) that have been claimed to benefit problem solving in a wide range of contexts.

One can find a variety of views in the literature regarding the relationship between logic and thought. Some writers have argued that people naturally reason logically, at least in their more rational moments, or that their logical intuitions are sound. Others have taken the position that logic, at least formal logic, has little to do with the way people actually reason...Whether or not people do naturally think logically, the teaching of logic has been a staple of higher education for a very long time. One of the reasons, though not the only one, for offering courses in logic has been the assumption that in learning the rules of logic one would improve one's ability to reason well.

I believe that knowledge of logic can be an aid to reasoning, especially to what I am calling justificatory reasoning. The sine qua non of a compelling argument, whether in the form of a mathematical proof, a legal summation, a theoretical interpretation of a scientific finding, or a justification of a personal belief, is logical consistency. It is through the teaching of logic that such essential concepts as entailment and validity can be made clear. Several investigators of problem solving, beginning perhaps with Polya, have argued that there are certain techniques that can be used to good effect on problems independently of their domains. Among the techniques, sometimes called heuristics, strategies, or rules-of-thumb, that have been proposed are the following.

—Strive to understand the problem. Problems are sometimes expressed very informally or even vaguely. It is important in such instances to gain a clear understanding of exactly what the nature of the problem is. Restating (paraphrasing) it in one's own terms can help. —Analyze ends and means. An attempt to articulate explicitly the problem's ends, or goals, and to identify various possible means of making progress toward them can also help clarify the problem situation and make a start toward solution. —Make assumptions explicit. Often problems are stated incompletely or ambiguously. When this is the case, it is important to identify the essential information that is missing and fill it in with the required assumption(s). When assumptions are necessary, it is also important to be explicit about the assumptions one is making, because they may differ from the tacit or stated assumptions of others, including those of whoever originated the problem statement. —Make a representation of the problem (e.g., a table, a figure), and of partial solutions. Nearly everyone who writes about problem solving agrees that it is a good idea to represent a problem in a suitable way. —Break the problem down into manageable subproblems. Complex problems usually can be decomposed into subproblems each of which is less daunting than the parent problem. In solving any of the subproblems one contributes to the solution of the parent problem, and sometimes such partial solutions can provide insights that will permit reorganizing the parent problem in a helpful way. —Work backward. Some problems have the characteristic that the desired end state is known (e.g., the classic river-crossing puzzles in which the goal is to get all the wolves and sheep safely across the river) and the problem is to devise a method for achieving that state. In such cases, it can sometimes be advantageous to work from the goal backward, as well as from the initial state forward. —Simplify. Problem solvers often tackle a complex problem by first considering a simplified version of it that preserves certain characteristics of the complex one. —Consider extreme cases. Sometimes it helps one get a grasp of a problem to modify it by greatly reducing the number of entities involved or by greatly multiplying it. —Find an analogous or more familiar problem.

Advocates of general-to-specific approaches tend to favor the teaching of general reasoning and problem-solving skills and strategies in courses separate from conventional courses and assume that what is learned will be applied appropriately in specific domains. Advocates of specific-to-general approaches tend to favor the teaching of thinking in the context of specific domains, so that students learn how to think in the process of acquiring traditional subject matter knowledge. Proponents of both views have an interest in transfer. Advocates of the first view want what is learned in a relatively domain-independent way to transfer to any domain in which one has occasion to work. Advocates of the second view want what is learned in the context of one specific domain to transfer to performance in other, especially closely related, domains.

Given the important roles that arguments (both formal and informal) play in our lives - in the formation, modification, and defense of beliefs - an inability to analyze and evaluate arguments is a serious impediment to good reasoning. I have already mentioned some knowledge of logic as an important aid to good reasoning. Such knowledge is essential to an ability to distinguish between valid and invalid formal arguments. There is a great deal of evidence in the literature that many people have difficulty in this respect. Of special relevance to the possibility of improving reasoning through instruction is the finding of a considerable degree of consistency in the types of errors that people make in syllogistic reasoning tasks. Certain logical forms are much more problematic than others for many people and tend to evoke consistent error patterns. Evidence also suggests that the conclusions that people draw are sometimes influenced by information that is irrelevant to those conclusions and that information that is relevant and at hand is sometimes ignored. To the extent that people can be taught to deal more competently with commonly problematic forms their reasoning should be improved.

Although there is no generally agreed-upon procedure for evaluating inductive or informal arguments, I think it is possible to identify some general principles that apply. A few that I have suggested elsewhere can be summarized as follows: "Understand the argument. Identify the key assertion that is made and the assertions that are offered in its support. Consider whether the supporting assertions are true and, if they are, whether they really make the key assertion more believable. Consider what true assertions can be made that tend to make the key assertion less believable. Decide whether the weight of the evidence favors the key assertion or its denial". Such a procedure does not guarantee that only arguments supporting true conclusions will be accepted, of course, but it does ensure that some notice is given to the possibility of evidence that runs counter to a conclusion; and the results of research indicate that this possibility is often overlooked or, worse, intentionally ignored.

The ability to judge the plausibility of claims that come to all of us every day from the media, from employers or employees, from teachers, from friends and acquaintances is essential to good reasoning. Some of these claims are essential components of arguments. In order to evaluate such arguments, to know whether to accept their conclusions, one must be able not only to judge the validity of the logic but also the tenability of the claims that serve as the premises.

The ability to estimate (quantities, magnitudes, durations, distances, frequencies, probabilities) is closely associated with - perhaps a component of - the quality of good judgment and extraordinarily useful in many contexts. It can help one check whether the results of calculations are in "the right ball park."

Being alert to the tendency to overestimate the completeness of information provided, or recalled, that is germane to a problem one is trying to solve or a decision one must make should motivate search for missing information and perhaps result in more effective performance of problem solving and decision-making tasks. Similarly, inasmuch as most arguments are expressed incompletely, recognition of this fact should produce a greater sensitivity to the need for assumptions to make such arguments complete as an important aspect of careful reasoning.

Uncertainty is among the more common features of the problems with which people have to deal in daily life. The same point holds with respect to the problems faced by organizations, communities, and nations. Seldom is all the information that is relevant to a problem that must be dealt with, or a decision that must be made, available to the problem solver or decision maker. To be an effective reasoner one must be able to take the fact of incomplete information into account. This means that gaps must be plugged with assumptions, estimations, actuarial data, or subjective probabilities. Moreover, good reasoning requires that one be aware of when and how one is resolving uncertainty and plugging information holes. Tacitly making assumptions without being aware of doing so can be problematic.

The ability to see things from perspectives other than one's own is normally in evidence in children by about the age of four or five years. The ability to look at a situation from a variety of perspectives - especially from the point of view of others who are likely to have values and frames of reference that differ from one's own - and the inclination to exercise it, undoubtedly differ considerably among older children and adults. Good reasoning, especially reasoning about other people, their beliefs, feelings, and actions, requires this ability and the exercise of it. Closely related, and also important, is the ability to think counterfactually, to engage in "what if" thinking, to explore in one's imagination probable or plausible consequences of behavior or possible courses of action.

Several investigators have stressed the importance of being able to manage (plan, monitor, and assess) one's own reasoning performance. Palincsar and Brown, among others, argue that selfmanagement, self-monitoring, and self-evaluation are important to effective learning in general. They also note that self-regulated learners are motivated to use their metacognitive knowledge and to take responsibility for their own learning. Being a good manager of one's own cognitive resources means being able to stay focused on a task, to maintain attention against distractions. It also means being able to gauge accurately one's knowledge, degree of understanding, level of expertise, limitations, and need for help. Experts are considerably more likely to make use of such metacognitive skills in the performance of cognitively demanding tasks than are novices.

Reflectiveness is treated by some writers as a disposition, attitude, or even character trait, and as one that is especially important to good reasoning. As a character trait, reflectiveness means being habitually in a reflective frame of mirW - being reflective with respect to material that one is attempting to understand, with respect to relationships, meanings, implications, and one's own understanding or level of comprehension of a situation. It means looking for relationships, connections, and analogies.

Impulsiveness, the antithesis of reflectiveness, has been identified as a significant impediment to good reasoning, and to the development of effective cognitive skills more generally. The idea that impulsiveness is a major problem finds support in the argument, advanced by several researchers, that people often draw conclusions on the basis of consideration of only a small fraction of the relevant evidence. Having considered enough information to provide the basis for a conclusion with which they are comfortable, they stop looking for additional information that could conceivably invalidate the conclusion they have drawn. Baron argues that insufficient search is the cause of many reasoning difficulties.

A good reasoner is a seeker of information. Many people believe that most children are inquisitive by nature. There are reasons to suspect, however, that schooling sometimes inhibits children's natural curiosity by discouraging the asking of questions. Children are unlikely to ask questions if they fear that doing so will expose their ignorance or make them appear unintelligent in the eyes of their classmates or teachers. That students do not, as a rule, ask many questions in class has been noted by several investigators. This suggests that a reasonable goal for teaching is the provision of an atmosphere in which questioning is not only tolerated, but encouraged, and where curiosity is rewarded.

Probably most people would claim that they want to have beliefs that are true. But presumably people vary with respect to the strength of this value. Some will try hard to bring beliefs into correspondence with evidence of which they are aware and will modify beliefs when newly acquired information indicates the need to do so; others will form beliefs on the basis of scanty evidence and will protect them from additional information that could threaten their tenability. Ideally, one not only should want to hold beliefs that are consistent with evidence at hand, but also should maintain a proactive attitude toward seeking evidence and a willingness to change one's mind - to revise conclusions one has drawn - in response to evidence that indicates the need for a change.

Searching for evidence, fairly evaluating what is found, judging the plausibility of claims, and other aspects of good reasoning can be hard work. It is much easier to come to conclusions quickly, without worrying much about whether the conclusions drawn would be justified if more evidence were found and considered. Not everyone is willing to expend the mental energy required to reason well. How to instill this willingness where it does not exist is a major challenge to teaching; at the very least, students need to be made aware that good reasoning is not something that one learns how to do easily and quickly and that practicing it requires commitment and effort.

What Do We Know About The Nature of Reasoning?, R. Sternberg

My goal in this chapter will be to discuss those things about reasoning that we know, if not for sure, at least, with very high confidence. In particular, I have attempted to extract from each chapter in this book at least one generalization about the field of reasoning that seems to be as close as we come in psychology to being "beyond debate."

However distinct or even balkanized reasoning may be as afield of psychological inquiry, there is no encapsulated "reasoning" module in the brain that is distinct from all other modules in the brain that are studied in other fields of cognitive science.... Thus, the goal of studying reasoning and its relation to the brain should not be to reinvent the phrenological approach of Franz Gall, who would have sought a particular set of bumps on the head corresponding to the location where reasoning takes place. For example, it seems beyond dispute that prefrontal regions are involved in reasoning. But these regions are involved in other higher cognitive processes as well, at the same time that reasoning is not limited to these areas. It is quite likely, for example, that learning occurring in the hippocampus or emotional responses in the amygdala affect and are affected by the processing happening in the prefrontal lobes. Our goal, therefore, should not be to construct some sort of geographical atlas of the structure of reasoning, but rather to map the neural pathways involved in the functioning of reasoning.

Working memory plays a central role in deductive and inductive reasoning... The working-memory model is neutral with respect to a number of different specific claims about how reasoning occurs. For example, if reasoning occurs through the use of rules, then one of the sources of difficulty in reasoning problems could be the number of rules and results of applications of rules that need to be held in working memory at one time. If reasoning occurs through the use of mental models, then a source of difficulty could be the number of models and intermediate results of the application of those models that needs to be held in working memory at one time...In sum, reasoning does not appear to be a set of processes that is distinct from working memory, but rather, a complex interaction of working memory with other dynamic processes. Memory is not superimposed on reasoning: It is part of reasoning.

People have a tendency toward confirmation bias. It has long been known that people show various content effects in their reasoning. Relatively recent research has suggested that better thinkers are more resistant to content effects, and especially, to belief-bias effects, than are others. Yet, everyone is susceptible in greater or lesser degree. One of the simple effects to which people are susceptible is confirmation bias, the tendency to seek evidence that confirms what people already believe...Confirmation bias is, in a sense, one of the most powerful problems the world faces today. Terrorists seek evidence to justify their attacks; respondents to their attacks seek evidence for why their responses are appropriate to the nature and magnitude of the threat...The problem is that it is often difficult to find any truth when people are so busy trying to prove what they believe rather than find the truth...Frighteningly, perhaps, court proceedings work the same way, at least in the United States. A verdict in a criminal case often depends much more on which of two attorneys - a prosecutor and a defense lawyer - can provide a more convincing set of arguments, rather than on what actually happened that led to the case in the first place.

Heuristics are common in everyday reasoning, and they can greatly facilitate or seriously impede the quality of that reasoning... Thinking about heuristics has undergone an evolutionary process over the years. Early research on reasoning suggested that they were mostly negative. For example, one of the classic articles in the field of reasoning suggested that people's errors in reasoning were largely due to an atmosphere effect whereby people tended to choose negative responses to syllogism problems with a negative in them, and particular responses to problems with particular quantifiers in them. Although Woodworth and Sells did not refer to the atmosphere effect as a heuristic, that is what it was...The early research was so strongly directed toward the negative effects of heuristics that it began to look as though shortcuts in reasoning were something like shortcuts in auditing - a recipe for disaster. Cohen showed that, in many respects, Tversky and Kahneman's view of heuristics was too negative - that heuristics could be viewed in a much more positive way than had been thought. More recently, Gigerenzer, Todd, and the ABC Research Group have shown that "fast and frugal" heuristics can have an enormously positive effect on reasoning. For example, the "takethe- best" heuristic, whereby one makes decisions on the basis of a single powerful criterion rather than an assortment of criteria of various degrees of power, often yields better decisions than do more complex decision rules.

Reasoning skill correlates positive with various measures of intelligence. It is not totally surprising perhaps that reasoning skills should correlate with intelligence because many definitions of intelligence have had reasoning either at the core or as an important supporting part of intelligence... In fact, reasoning has been at the core of how psychologists interpret intelligence even going back to Spearman, arguably the first great theorist of intelligence. Spearman proposed a theory of intelligence based on the processes used in analogical reasoning, namely, encoding of analogy terms (what he called "apprehension of experience"), inference of the relation between the first two analogy terms (what he called "education of relations"), and application of the inferred relation to the second two analogy terms (what he called "education of correlates").

In sum, although many issues in the study of reasoning are contentious, not all are. The fact that many issues are contentious is not a bad sign but a good one. The field of reasoning is alive and vibrant and is moving forward at a rapid clip. The fact that at least some issues are resolved to most people's satisfaction is also a good sign. The field is solving puzzles as well as creating new ones.

What is Induction and Why Study It?, E. Heit

Why study induction, and indeed, why should there be a whole book devoted to the study of induction? The first reason is that inductive reasoning corresponds to probabilistic, uncertain, approximate reasoning, and as such, it corresponds to everyday reasoning. On a daily basis we draw inferences such as how a person will probably act, what the weather will probably be like, and how a meal will probably taste, and these are typical inductive inferences. So if researchers want to study a form of reasoning that is actually a pervasive cognitive activity, then induction is of appropriate interest.

The study of induction has the potential to be theoretically revealing. Because so much of people's reasoning is actually inductive reasoning, and because there is such a rich data set associated with induction, and because induction is related to other central cognitive activities, it is possible to find out a lot about not only reasoning but cognition more generally by studying induction.

Induction is traditionally contrasted with deduction, which is concerned with drawing logically valid conclusions that must follow from a set of premises. The following section will consider possible definitions of induction by describing possible relations between induction and deduction. But first it is useful to briefly mention that the reasons for studying induction to some extent are linked to the differences between induction and deduction. That is, it could be argued that induction, in comparison to deduction, characterizes more of everyday reasoning, has the potential to be studied with a broader range of tasks and materials, and is closely related to other cognitive activities that help people manage uncertainty.

Before assessing to what extent induction and deduction are similar or different, it is first important to consider just what kind of entities induction and deduction are. Although not always made explicit by researchers, there are two views on this issue, namely, the "problem view" and the "process view." According to the problem view, induction and deduction refer to particular types of reasoning problems. So from looking at a particular problem, say a question on a piece of paper in a psychological experiment on reasoning, it should be possible to say whether this is an induction problem or a deduction problem (or possibly it could be deemed debatable whether it is one or the other). In contrast, according to the process view, the locus of the question is not on the paper but in the head. That is, induction and deduction refer to psychological processes. For a given problem, it may be possible to answer it using induction processes or deduction processes. Likewise, we can investigate what is the relation between the two kinds of processing.

It is sometimes said that induction goes from the specific to the general, and deduction goes from the general to the specific. For example, after observing that many individual dogs bark, one might induce a more general belief that all dogs bark. Alternately, having the general belief that all dogs bark, one might deduce that some particular dog will bark. However, there are difficulties with this version of the problem view.... The key point is that one can't just look at the written form of an argument, in terms of whether it goes from specific to general or vice versa, and easily state whether it is inductive or deductive in nature.

Hence, it would seem profitable to take a more subtle approach to the problem view. Perhaps the most defensible version of the problem view is to define deductively valid arguments, and relate other kinds of arguments to those that are deductively valid. One standard definition of deductively valid arguments is that these are arguments following the rules of a well-specified logic. Assuming that one can specify the rules of one's preferred logic, say in terms of truth tables for various symbolic combinations, then it should be possible (if not easy) to determine whether any given argument is deductively valid or not. It might be seen as a small disadvantage of this approach that deductive validity is not defined in absolute terms but only relative to a logic. Different people might endorse different logics and hence disagree about which arguments are deductively valid. On the other hand, defining deductive validity relative to a logic could be seen as an advantage in terms of giving flexibility and in terms of appreciating that there is not a single true logic that is universally agreed. A more serious problem with this version of the problem view is that it does not say much about inductive problems. Once the deductively valid arguments are defined, what remains are the deductively invalid ones. Presumably some of these are stronger than others, in terms of induction.

Studies of induction typically ask people to make judgments of argument strength, such as to judge which of two arguments is stronger, or with a single argument to make a continuous judgment of strength or probability. In comparison to induction, research in deduction has used a narrower range of problems. One typical area of research within deduction is conditional reasoning - arguments involving ifs and thens, examining reasoning involving classic rules such as modus ponens and modus tollens.... Research on deduction tends to ask people to assess logical validity of conclusions (a yes or no question) rather than make continuous judgments. Overall, the conventional approach is like other approaches to the problem view in that there is a relatively narrow range of arguments corresponding to deduction and a wider, somewhat ill-defined, range corresponding to induction.

Perhaps the most appealing aspect of the problem view is that it offers the possibility of defining induction and deduction in an objective way, in terms of the problem being solved or the question being asked. (The problem view is more impressive in terms of defining deduction in comparison to defining induction, though.) From the point of view of psychologists, this strength would also be the greatest weakness, namely, that the problem view does not itself refer to psychological processes. Just because one problem is defined as an induction problem and another is defined as a deduction problem does not guarantee that people will engage in inductive reasoning processes for one task and deductive reasoning processes for the other task. The same processes could be used for both, or the delimitation between types of psychological processes might not correspond at all to the agreed definition of problems, or any problem might engage a mixture of processes. In the terminology of memory research, there are no process-pure tasks. Of course, for computer scientists or logicians, reference to psychological processes may not be a priority. Still, it does seem desirable to consider the alternative of treating induction and deduction as possible kinds of psychological process.

According to the process view, comparing induction and deduction is a matter of specifying the underlying psychological processes. According to oneprocess accounts, the same kind of processing underlies both induction and deduction. Another way to describe this idea is that there is essentially one kind of reasoning, which maybe applied to a variety of problems that could be considered either inductive or deductive in nature. In contrast, according to two-process accounts, there are two distinct kinds of reasoning. It is possible that these two kinds of reasoning directly correspond to induction and deduction. Alternately, the two kinds of reasoning might correspond to some other distinction, such as intuitive reasoning versus deliberative reasoning, that could be related to the distinction between induction and deduction. It should be acknowledged at the start that one-process and two-process accounts are somewhat poorly named. That is, at some level, reasoning surely involves many different psychological processes. The question, though, is whether the same processing account is applied to both induction and deduction, or whether two different processing accounts are applied.

One of the most widely known theories of reasoning is mental model theory, which proposes that people solve reasoning problems extensionally by constructing models of possible states ofthe world and performing operations and manipulation on them. Mental model theory is usually thought of as an account of deduction, and indeed it has been extensively applied to conditional-reasoning and syllogisticreasoning problems. However, it has also been argued that mental model theory can be applied to problems of induction, namely, probabilistic reasoning tasks. Hence, mental model theory is a one-process account, in the sense that it is aimed at giving a singular account for problems both of induction and deduction.

In contrast to one-process accounts, other researchers have emphasized a distinction between two kinds of reasoning. In these two-process accounts there is one system that is relatively fast but heavily influenced by context and associations, and another system that is more deliberative and analytic or rule based. These two systems do not necessarily correspond directly to induction and deduction. That is, the traditional distinction between these two forms of reasoning may not be the best way to divide things in psychological terms. Still, it is plausible that induction would depend more on the first system, whereas deduction would depend more on the second system. These two-process accounts have been used to explain a variety of findings in reasoning, concerning individual differences, developmental patterns, and relations between reasoning and processing time. For example, in Stanovich's work there is a rich account of how reasoning in the more deliberative system is correlated with IQ, accounting for patterns of individual differences in a variety of problems that would rely more on one system or the other.

There is some neuropsychological evidence, based on brain imaging, for two anatomically separate systems of reasoning. In the studies, subjects were given a set of arguments to evaluate. Half the subjects were asked to judge deductive validity and the other half were asked to judge inductive plausibility. Within each study, there were distinct brain areas implicated for deduction versus induction. What is particularly relevant for present purposes is that the problems were the same for the two conditions, but subjects were asked to perform either deduction or induction. Hence, this is a case of unconfounding the process view from the problem view - presumably all that varied between conditions was processes, unlike the situation in most previous studies of deduction, induction, or both, which used very different problems for one task or the other.

In sum, there is some evidence already that giving people deduction versus induction instructions leads to qualitatively different results. It would seem difficult to explain these results by assuming that deduction and induction processes are essentially the same, except that deduction involves a stricter criterion for giving a positive response. Yet at the same time, it seems too early to abandon the one-process accounts, which do provide detailed and accurate predictions about a range of phenomena, usually either concerning deductive or inductive problems. In contrast, the two-process view does not seem to be as well developed in terms of providing detailed process accounts and predictions. More experimentation, directly aimed at comparing the oneand two-process views and at further developing the two-process view, is clearly needed.

The focus of the remainder of this chapter will be the diversity principle, namely, the idea that more diverse evidence seems to be stronger evidence than less diverse evidence. This principle seems to be ubiquitous in various forms of reasoning. For example, in social reasoning, seeing a person act in an extroverted way, in a variety of contexts, suggests that the person is truly extroverted by nature. In comparison, seeing a person repeatedly act in an extroverted way, but only in one context, does not give as good support for inferences that the person is truly extroverted. In legal reasoning, having two independent witnesses to a crime seems to be stronger evidence than two witnesses who may share a similar perspective, such as two members of the same family. Note that none of this represents anything like a deductively valid inference; however, there is still a sense of stronger evidence coming from more diverse observations.

The diversity principle has been an object of interest in terms of various approaches to induction, including the historical approach, the philosophical approach, the experimental approach, the developmental approach, and the model-based approach. These approaches will be reviewed in relation to how they have addressed the diversity principle. The diversity principle has been historically important in science. Scientists have tended to favor testing a theory with a diverse set of experiments rather than repeatedly conducting the same experiment or close replications. Imagine two scientists who are testing their respective theories. One scientist essentially conducts the same experiment ten times, whereas the other conducts a variety of experiments assessing different aspects of the theory. Which theory will seem to have stronger support?

This historical approach is complemented by attempts of philosophers and statisticians to argue that certain patterns of induction are normative or correct. The philosophical approach follows in the footsteps of Hume's problem of induction, namely, the problem of whether an inductive inference can ever be justified or considered valid. Without solving Hume's problem in absolute terms, it still might be possible to argue that performing induction in one way is better than another. As such, there have been various attempts to argue for or even prove the greater strength of diverse evidence in comparison to less diverse evidence.

For example, Nagel argued that a scientific theory should be derived from diverse observations to obtain more reliable estimates. He gave the example of inspecting the quality of coffee beans delivered on a ship. It would be better to inspect small samples of beans from various parts of the ship than to inspect a large number of beans from just one location. Carnap linked the collection of diverse evidence to the principle that scientific theories should make novel predictions rather than merely redescribe old data. Similarly, Hempel related the collection of diverse evidence to a falsifying research strategy, namely, it is better to test theories with a wide variety of challenging experiments.

Medin, Coley, Storms, and Hayes reported further exceptions to the diversity principle. One exception, referred to as non-diversity by property reinforcement, potentially makes a direct challenge to the diversity principle that is not as easily explained in terms of the use of other knowledge. The idea behind non-diversity by property reinforcement is that two diverse categories may nonetheless have some characteristic in common and tend to generalize only to other categories with this same characteristic. In the non-diversity by property reinforcement effect, "if an otherwise diverse set of premises shares a salient property not shared by the conclusion category, the reinforcement of the property might weaken that argument relative to a related argument with less diverse premises".

By their very nature, inductive inferences do not have a "right answer" in the same way as deductive inferences. Yet there are still regularities, such as the diversity principle, which can be studied from a variety of perspectives, including historical, philosophical, experimental, developmental, and computational. By no means is this regularity completely deterministic; indeed, there are well-documented exceptions to the diversity principle that are themselves of interest.

Abductive Inference: From Philosophical Analysis to Neural Mechanisms, P. Thagard

In the 1890s, the great American philosopher C. S. Peirce used the term "abduction" to refer to a kind of inference that involves the generation and evaluation of explanatory hypotheses. This term is much less familiar today than "deduction" which applies to inference from premises to a conclusion that has to be true if the premises are true. And it is much less familiar than "induction," which sometimes refers broadly to any kind of inference that introduces uncertainty, and sometimes refers narrowly to inference from examples to rules, which I will call "inductive generalization." Abduction is clearly a kind of induction in the broad sense, in that the generation of explanatory hypotheses is fraught with uncertainty. For example, if the sky suddenly turns dark outside my window, I may hypothesize that there is a solar eclipse, but many other explanations are possible, such as the arrival of an intense storm or even a huge spaceship.

In everyday life, abductive inference is ubiquitous, for example when people generate hypotheses to explain the behavior of others, as when I infer that my son is in a bad mood to explain a curt response to a question. Detectives perform abductions routinely in order to make sense of the evidence left by criminal activity, just as automobile mechanics try to figure out what problems are responsible for a breakdown. Physicians practice abduction when they try to figure out what diseases might explain a patient's symptoms... Abduction occurs in many other domains as well, for example, religion, where people hypothesize the existence of God in order to explain the design and existence of the world.

First, I want to examine the nature of abduction and sketch what would be required for a full psychological theory of it. I then outline a neurocomputational theory of abductive inference that provides an account of some of the neural processes that enable minds to make abductive inference. Finally, I discuss the more general implications of replacing logic-based philosophical analyses of human inference with theories of neural mechanisms.

Here are the typical stages in the mental process of abduction. First, we notice something puzzling that prompts us to generate an explanation. It would be pointless to waste mental resources on something ordinary or expected. For example, when my friends greet me with the normal "Hi," I do not react like the proverbial psychoanalyst who wondered "What can they mean by that?" In contrast, if a normally convivial friend responds to "Good morning" with "What's so good about it?" I will be prompted to wonder what is currently going on in my friend's life that might explain this negativity. Peirce noticed that abduction begins with puzzlement, but subsequent philosophers have ignored the fact that the initiation of this kind of inference is inherently emotional. Intense reactions such as surprise and astonishment are particularly strong spurs to abductive inference. Hence the emotional initiation of abductive inference needs to be part of any psychological or neurological theory of how it works. An event or general occurrence becomes a target for explanation only when it is sufficiently interesting and baffling.

Second, the mind searches for possible hypotheses that could explain the target. Sometimes, the search is easily completed when there is a prepackaged hypothesis waiting to be applied. For example, if you know that your friend Alice gets stressed out whenever she has a deadline to meet, you might explain her grumpy behavior by the conjecture that she has a project due. In more deeply puzzling cases, the search for an explanatory hypothesis may require a much longer search through memory, or even the use of analogy or other constructive processes to generate a highly novel hypothesis. This generation is what happens in science when a genuinely new theory needs to be developed. Generation of a candidate explanatory hypothesis is the usual third stage of abductive inference. If one is epistemically lazy, abductive inference may end with the generation of a single candidate. But scientists and careful thinkers in general are aware of the perils of abductive inference, in particular that one should not accept an explanatory hypothesis unless it has been assessed with respect to competing hypotheses and all the available evidence. Philosophers call this fourth, evaluative stage of abductive reasoning inference to the best explanation. Ideally, the reasoner correctly decides that it is legitimate to infer a hypothesis because it really is the best explanation of all the available evidence. Thus, generation of an explanatory hypothesis blends into its evaluation. Just as abduction originates with an emotional reaction, it ends with one, because formation and acceptance of explanatory hypotheses usually produce positive emotions. Hence we can mark emotional satisfaction as the final stage of abductive inference.

Psychologists rarely use the terms "abduction" or "abductive inference," and very little experimental research has been done on the generation and acceptance of explanatory hypotheses. Much of the psychological literature on induction concerns a rather esoteric pattern of reasoning, categorical induction, in which people express a degree of confidence that a category has a predicate after being told that a related category has the predicate.

The structure of abduction is roughly this: There is a puzzling target T that needs explanation. Hypothesis H potentially explains T. So, H is plausible. H is a better explanation of T and other phenomena than competing hypotheses. So H is acceptable. It would be psychologically unrealistic, however, to assume, as philosophers and AI researchers have tended to do, that T and H must be sentences or propositions (the meanings of sentences). A broader view of mental representation is required. As already mentioned, abductive inference can be visual as well as verbal.

It is an interesting question whether hypotheses can be represented using all sensory modalities. For vision the answer is obvious, as images and diagrams can clearly be used to represent events and structures that have causal effects. And the answer appears to be yes when one is explaining one's own behavior: I may recoil because something I touch feels slimy, or jump because of a loud noise, or frown because of a rotten smell, or gag because something tastes too salty. Hence in explaining my own behavior, my mental image of the full range of examples of sensory experiences may have causal significance. Applying such explanations of the behavior of others requires projecting onto them the possession of sensory experiences that I think are like the ones that I have in similar situations.

Empathy works the same way, when I explain people's behavior in a particular situation by inferring that they are having the same kind of emotional experience that I have had in similar situations. For example, if a colleague with a recently rejected manuscript is frowning, I may empathize by remembering how annoyed I felt when a manuscript of mine was rejected, and my mental image projected onto the colleague constitutes a non-verbal representation that explains the frown....Hence there is reason to believe that abductive inference can be fully multimodal, in that both targets and hypotheses can have the full range of verbal and sensory representations. In addition to words, sights, sounds, smells, touches, and tastes, these can include emotional feelings, kinesthetic experiences such as feeling the body arranged in a certain way, and other feelings such as pain.

Abductive inference is from a target to a hypothesis that explains it, but what is explanation? In philosophy and cognitive science, there have been at least six approaches to the topic of explanation. Explanations have been viewed as deductive arguments, statistical relations, schema applications, analogical comparisons, causal relations, and linguistic acts. All of these approaches have illuminated some aspects of the practice of explanation in science and everyday life, but the core of explanation, I would argue, is causality: a hypothesis explains a target if it provides a causal account of what needs to be explained. In medicine, a disease explains symptoms because the abnormal biological state that constitutes the disease produces the symptoms through biological mechanisms. In ordinary social life, attributing a mental state such as an emotion explains a person's behavior because the mental state is the assumed cause of the behavior. In science, a theory explains phenomena such as the motions of the planets by providing the causes of such phenomena. Deductive, statistical, schematic, analogical, and linguistic aspects of explanation can all be shown to be subordinate to the fundamental causal aspect of explanation.

The philosophical literature on causality is huge, but here is a quick summary of extant positions on the nature of causality: 1. Eliminativist: Causality is an outmoded notion no longer needed for scientific discourse. 2. Universalist: Causation is a relation of constant conjunction: the effect always occurs when the cause occurs. 3. Probabilistic: Causation is a matter of probability: the effect is more probable given the cause than otherwise. 4. Causal powers: the cause has a power to produce the effect.

Recent work using functional magnetic resonance imaging has investigated brain mechanisms underlying perceptual causality. Participants imaged while viewing causal events had higher levels of relative activation in the right middle frontal gyrus and the right inferior parietal lobule compared to those viewing non-causal events. The evidence that specific brain structures are involved in extracting causal structure from the world fits well with cognitive and developmental evidence that adults and children are able to perceive causal relations, without making inferences based on universality, probability, or causal powers. It is therefore plausible that people's intuitive grasp of causality, which enables them to understand the distinction between causal relations and mere co-occurrence, arises very early from perceptual experience. Of course, as people acquire more knowledge, they are able to expand this understanding of causality far beyond perception, enabling them to infer that invisible germs cause disease symptoms. But this extended understanding of causality is still based on the perceptual experience of one event making another happen, and does not depend on a mysterious, metaphysical conception of objects possessing causal powers.

On the standard philosophical view, inference is the movement from one or more propositions taken to be true to another proposition that follows from them deductively or inductively. Here a proposition is assumed to be an abstract entity, namely, the meaning content of a sentence. Belief and other mental states such as doubt, desire, and fear are all prepositional attitudes, that is, relations between persons and propositions. An inference is much like an argument, which is the verbal description of a set of sentential premises that provide the basis for accepting a conclusion. Most philosophical and computational accounts of abductive inference have assumed this kind of linguistic picture of belief and inference.

What then is inference? Most generally, inference is a kind of transformation of neural structures, but obviously not all such transformations count as inference. We need to isolate a subclass of neural structures that are representations, that is, ones that stand for something real or imagined in the world. Roughly, a neural structure is a representation if its connections and spiking behavior enable it to relate to perceptual input and/or the behavior of other neural structures in such a way that it can be construed as standing for something else such as a thing or concept.

Accordingly, we can characterize inference as the transformation oj'representational neural structures. Inference involving sentences is a special case of such transformation where the relevant neural structures correspond to sentences. My broader account has the great advantage of allowing thinking that uses visual and other sensory representations to count as inference as well. From this perspective, abduction is the transformation of representational neural structures that produces neural structures that provide causal explanations.

Inferences about what to do are usually initiated by either positive or negative emotions. Decisions are sometimes prompted by negative emotions such as fear: if I am afraid that something bad will happen, I may be spurred to decide what to do about it... More positively, emotions such as happiness can lead to decisions, as when someone thinks about how much fun it would be to have a winter vacation and begins to collect travel information that will produce a decision about where to go. Just as people do not make abductive inferences unless there is some emotional reason for them to look for explanations, people do not make inference about what to do unless negative or positive emotional reactions to their current situation indicate that action is required.

Analogical inference often involves emotional content, especially when it is used in persuasion to transfer negative affect from a source to a target. For example, comparing a political leader to Hitler is a common way of motivating people to dislike the leader. Such persuasive analogies are often motivated by emotional reactions such as dislike of a person or policy. Because I dislike the leader, I compare him or her to Hitler in order to lead you to dislike the leader also.

Are inductive generalizations initiated by emotional reactions? At the least, emotion serves to focus on what is worth the mental effort to think about enough to form a generalization. As a social example, if I have no interest in Albanians, I will probably not bother to form a stereotype that generalizes about them, whereas if I strongly like or dislike them I will be much more inclined to generalize about their positive or negative features. I conjecture that most inductive generalizations occur when there is some emotion-related interest in the category about which a rule is formed.

Much of scientific theorizing consists of generating new ideas about unobservable mechanisms. For example, medical researchers develop mechanistic models of how the metabolic system works in order to explain the origins of diseases such as diabetes. Often, such theorizing requires postulation of objects, relations, and changes that are not directly observed. In such cases, knowledge about mechanisms cannot be obtained by inductive generalization of the sort that works with bicycles, but depends on abductive inference in which causal patterns are hypothesized rather than observed. This kind of abduction to mechanisms is obviously much more difficult and creative than abduction from already understood mechanisms. Often it involves analogical inference in which a mechanism is constructed by comparing the target to be explained to another similar target for which a mechanism is already understood. In this case, a mechanism is constructed by mapping from a similar one.

In sum, abduction is multimodal in that can operate on a full range of perceptual as well as verbal representations. It also involves emotional reactions, both as input to mark a target as worthy of explanation and as output to signal satisfaction with an inferred hypothesis. Representations are neural structures consisting of neurons, neuronal connections, and spiking behaviors. In abduction, the relation between hypotheses and targets is causal explanation, where causality is rooted in perceptual experience. Inference is transformation of representational neural structures. Such structures are mechanisms, and abductive inference sometimes applies knowledge of mechanisms and more rarely and valuably generates new hypotheses about mechanisms.

The Place of Analogy in Cognition, K. Holyoak, D. Gentner, B. Kokinov

What cognitive capabilities underlie our fundamental human achievements? Although a complete answer remains elusive, one basic component is a special kind of symbolic ability—the ability to pick out patterns, to identify recurrences of these patterns despite variation in the elements that compose them, to form concepts that abstract and reify these patterns, and to express these concepts in language. Analogy, in its most general sense, is this ability to think about relational patterns. As Douglas Hofstadter argues, analogy lies at the core of human cognition.

In contrast to any other type of animal, analogy use develops spontaneously in very young members of the human species. The ability to perceive and explicitly represent relational patterns thus appears to be intimately connected to the development of general representational abilities in humans.

The more complex the analogies, the more complex the representations they require. To draw an analogy, whole systems of connected relations are matched from one domain to another. To model this process, computational models must be able to build and maintain complex representational structures. Although this requirement is easily satisfied in models that make use of explicit symbols for individual concepts, it is much more difficult to satisfy it using models that represent symbols as patterns of activation over a neural substrate. Solving this representational problem is one of the major goals for current modeling efforts...Presumably, this difficult problem was solved in some manner during the evolution of the primate nervous system. Although we know little as yet about the neural substrate for processing relational patterns, progress has been made in understanding the cognitive operations involved.

Although analogy has likely been a human cognitive ability for tens of thousands of years, its direct expression in the historical record awaited the development of written language. Uses of analogies—explicit mention of relational likenesses between distinct situations—are found in the world's earliest preserved literature.

In the Babylonian epic Gilgamesh, written about four thousand years ago, the hero grieves over the corpse of his friend Enkidu: . . . Gilgamesh covered Enkidu's face with a veil like the veil of a bride. He hovered like an eagle over the body, or as a lioness does over her brood.

In ancient India, more than 2,500 years ago, concrete analogies were used to express abstract philosophical ideas. For example, in the Upanishads it is written that, "As a man in sexual union with his beloved is unaware of anything outside or inside, so a man in union with Self knows nothing, wants nothing, has found his heart's fulfillment and is free of sorrow."

Analogies have figured in poetry across all times and cultures. One basic function of analogy—perhaps its most ancient—is especially apparent in poetry. This is the transfer of emotions, a topic discussed by Paul Thagard and Cameron Shelley. The Babylonian text makes us feel that Gilgamesh's grief is as profound as the love of a bridegroom for his bride, his watchfulness and protectiveness as intense as those of an eagle or a lioness...And the Indian poet uses his analogy with the experience of sexual union to convey not only an intellectual sense of what it means to be connected with the Self, but even more forcefully the emotional intensity of the experience. Emotional experiences are notoriously difficult or impossible to convey by literal language; but by connecting the relational pattern of a novel experience with that of a familiar, emotion-laden one, analogy provides a way of recreating a complex pattern of feelings.

The progression from highly specific, single-case analogies to more abstract concepts or schemas is one of the most powerful roles that analogy plays in cognition. This progression has been observed not only for scientific, mathematical, and problem-oriented concepts, but also for metaphorical concepts in everyday language.

In psychology, Centner began working on mental models and analogy in science. She was struck by the idea that in analogy, the key similarities lie in the relations that hold within the domains (e.g., the flow of electrons in an electrical circuit is analogically similar to the flow of people in a crowded subway tunnel), rather than in features of individual objects (e.g., electrons do not resemble people). Moreover, analogical similarities often depend on higherorder relations—relations between relations. For example, adding a resistor in series to a circuit causes (a higher-order relation) a decrease in flow of electricity, just as adding a narrow gate in the subway tunnel would decrease the rate at which people pass through. In her structuremapping theory, Centner set forth the view that analogy entails finding a structural alignment, or mapping, between domains. This alignment between two representational structures is characterized by structural parallelism (consistent, one-to-one correspondences between mapped elements) and systematicity—an implicit preference for deep, interconnected systems of relations governed by higher-order relations, such as causal, mathematical, or functional relations.

Gick and Holyoak provided evidence that analogy can provide the seed for forming new relational categories, by abstracting the relational correspondences between examples into a schema for a class of problems. Analogy was viewed as a central part of human induction. Holyoak and Thagard developed a multiconstraint approach to analogy in which similarity, structural parallelism, and pragmatic factors interact to produce an interpretation. They developed simulation models of analogical mapping and inference and retrieval based on algorithms for simultaneously satisfying multiple constraints.

The process of analogical thinking can be usefully decomposed into several basic constituent processes. In a typical reasoning scenario, one or more relevant analogs stored in long-term memory must be accessed. A familiar analog must be mapped to the target analog to identify systematic correspondences between the two, thereby aligning the corresponding parts of each analog. The resulting mapping allows analogical inferences to be made about the target analog, thus creating new knowledge to fill gaps in understanding. These inferences need to be evaluated and possibly adapted to fit the unique requirements of the target. Finally, in the aftermath of analogical reasoning, learning can result in the generation of new categories and schemas, the addition of new instances to memory, and new understandings of old instances and schemas that allow them to be accessed better in the future. All current computational models of analogy deal with some subset of these basic component processes, and progress has been made in integrating them.

Emotional Analogies and Analogical Inference, P. Thagard, C. Shelley

Despite the growing appreciation of the relevance of affect to cognition, analogy researchers have paid remarkably little attention to emotion. This paper discusses three general classes of analogy that involve emotions. The most straightforward are analogies and metaphors about emotions, for example, "Love is a rose and you better not pick it." Much more interesting are analogies that involve the transfer of emotions, for example, in empathy in which people understand the emotions of others by imagining their own emotional reactions in similar situations. Finally, there are analogies that generate emotions, for example, analogical jokes that generate emotions such as surprise and amusement.

In logic books, analogical inference is usually presented by a schema such as the following: Objects of type X have properties G, H, etc. Objects of type Y have properties G, H, etc. Objects of type X have property F. Therefore: Objects of type Y have property F. For example, when experiments determined that large quantities of the artificial sweetener saccharine caused bladder cancer in rats, scientists analogized that it might also be carcinogenic in humans. Logicians additionally point out that analogical arguments may be strong or weak depending on the extent to which the properties in the premises are relevant to the property in the conclusion.

Moreover, the prevalent models of analogy encode information symbolically and assume that what is inferred is verbal information that can be represented in prepositional form by predicate calculus or some similar representational system. As section 10.5 documents, analogical inference often serves to transfer an emotion, not just the verbal representation of an emotion.

Thagard proposes a theory of emotional coherence that has applications to numerous important psychological phenomena such as trust. This theory makes the following assumptions about inference and emotions: 1. All inference is coherence based. So-called rules of inference such as modus ponens do not by themselves license inferences, because their conclusions may contradict other accepted information. The only rule of inference is: Accept a conclusion if its acceptance maximizes coherence. 2. Coherence is a matter of constraint satisfaction, and can be computed by connectionist and other algorithms. 3. There are six kinds of coherence: analogical, conceptual, explanatory, deductive, perceptual, and deliberative. 4. Coherence is not just a matter of accepting or rejecting a conclusion, but can also involve attaching a positive or negative emotional assessment to a proposition, object, concept, or other representation. From this coherentist perspective, all inference is defeasible and holistic and differs markedly from logical deduction in formal systems. Philosophers who have advocated coherentist accounts of inference include Bosanquet and Harman.

It is not surprising that writers discuss emotions nonliterally, because it is very difficult to describe the experience of emotions in words. In analogies about emotions, verbal sources help to illuminate the emotional target, which may be verbally described but which also has an elusive, nonverbal, phenomenological aspect. Analogies are also used about negative emotions: anger is like a volcano, jealousy is a green-eyed monster, and so on.

Just as it is hard to verbalize the general character of an emotion, it is often difficult to describe verbally one's own emotional state. Victims of post-traumatic stress disorder frequently use analogies and metaphors to describe their own situations: • I am a time bomb ticking, ready to explode. • I feel like I am caught up in a tornado. • I am a rabbit stuck in the glare of headlights who can't move. • My life is like a rerun of a movie that won't stop. • I feel like I'm in a cave and can't get out.

The purpose of analogies about emotions is often explanatory, describing the nature of a general emotion or a particular person's emotional state. But analogy can also be used to help deal with emotions, as in the following quote from Nathaniel Hawthorne: "Happiness is a butterfly, which, when pursued, is always just beyond your grasp, but which, if you will sit down quietly, may alight upon you." People are also given advice on how to deal with negative emotions, being told for example to "vent" their anger, or to "put a lid on it."

Analogies can involve transfer of emotions from a source to a target. There are at least three such kinds of emotional transfer, involved in persuasion, empathy, and reverse empathy. In persuasion, I may use an analogy to convince you to adopt an emotional attitude. In empathy, I try to understand your emotional reaction to a situation by transferring to you my emotional reaction to a similar situation. In reverse empathy, I try to get you to understand my emotion by comparing my situation and emotional response to it with situations and responses familiar to you.

The purpose of many persuasive analogies is to produce an emotional attitude, for example when an attempt is made to convince someone that abortion is abominable or that capital punishment is highly desirable. If I want to get someone to adopt positive emotions toward something, I can compare it to something else toward which he or she already has a positive attitude. Conversely, I can try to produce a negative attitude by comparison with something already viewed negatively.

Similarity is one of the constraints that influence how two analogs are mapped to each other, including both the semantic similarity of predicates and the visual similarity of objects. We conjecture that emotional similarity may also influence analogical mapping and predict that people will be more likely to map elements that have the same positive or negative valence.

Another, more personal, kind of persuasive emotional analogy is identification, in which you identify with someone and then transfer positive emotional attitudes about yourself to them. According to Fenno, members of the U.S. congress try to convey a sense of identification to their constituents. The message is, "You know me, and I'm like you, so you can trust me."

A third class of emotional analogies involves ones that are not about emotions and do not transfer emotional states, but rather serve to generate new emotional states. There are at least four subclasses of emotiongenerating analogies, including humor, irony, discovery, and motivation. One of the most enjoyable uses of analogy is to make people laugh, generating the emotional state of mirth or amusement. A major part of what makes an analogy funny is a surprising combination of congruity and incongruity.In analogical jokes, the unusual mapping produces surprise because it connects together elements not previously mapped, but does so in a way that is still highly coherent. The combination of activation of the surprise node, the coherence node, and other emotions generates humorous amusement.

Analogies that are particularly deep and elegant can also generate an emotion similar to that produced by beauty. A beautiful analogy is one so accurate, rich, and suggestive that it has the emotional appeal of an excellent scientific theory or mathematical theorem. Holyoak and Thagard describe important scientific analogies such as the connection with Malthusian population growth that inspired Darwin's theory of natural selection. Thus scientific and other elegant analogies can generate positive emotions such as excitement and joy without being funny.

The final category of emotion-generating analogies we want to discuss is motivational ones, in which an analogy generates positive emotions involved in inspiration and self-confidence. Lockwood and Kunda have described how people use role models as analogs to themselves, in order to suggest new possibilities for what they can accomplish. For example, an athletic African American boy might see Michael Jordan as someone who used his athletic ability to achieve great success. By analogically comparing himself to Michael Jordan, the boy can feel good about his chances to accomplish his athletic goals. Adopting a role model in part involves transferring emotions, for example, transferring the positive valence of the role model's success to one's own anticipated success, but it also generates new emotions accompanying the drive and inspiration to pursue the course of action that the analogy suggests.

Inferential analogies were further divided into two types: "hot" and "cold." Hot analogies serve to transfer emotional tags or attitudes from the source to target, whereas cold analogies serve simply to transfer structured information without producing any particular affect. Hot analogies were further broken down into the three types of emotional analogies discussed above, namely empathy, reverse empathy, and persuasion. Very often the analogies conveyed in each news article were complex and appeared to serve more than one of the functions listed here. However, we counted each analogy only once on the basis of its most salient function.

Persuasive emotional analogies usually serve not to communicate an emotion between people of varied experience, but to have one person transfer some emotional attitude from one concept to another. For example, in order-te-persuade people to feel calm about an apparently dangerous situation, you might remind them of analogous situations that they regard calmly.

Reasoning: Philosophical Foundations, J. Adler

Deductive validity is monotonic: A valid argument cannot be converted into an invalid argument by adding additional premises. But an inductively good argument is nonmonotonic: new premises alone can generate an argument that is not good... In either argument, there is a reasoned transition in thought. The person who draws the inference, takes the premises as his reasons to believe the conclusion.

Grice draws the connection between reasons and reasoning by noting that if reason is the faculty which "equips us to recognize and operate with reasons" then we should also think of it as the faculty which "empowers us to engage in reasoning." Elaborating, he writes "if reasoning should be characterizable as the occurrence or production of a chain of inferences, and if such chains consist in (sequentially) arriving at conclusions which are derivable from some initial set of premises of which, therefore, these premises are ... reasons, the connection between the two ideas is not accidental."

Induction and deduction supply reasons to believe, since each seeks to preserve the truth of its premises, while extending them to new truths acquired as beliefs. Beliefs are the product of reasoning since belief aims at truth. The end result in belief explains why reasoning matters so profoundly to us. We care to get correct conclusions both intrinsically, since that is what having a belief claims, but also, and more obviously, extrinsically. Belief guides actions, and actions are expected to succeed (reach their goal) only if the beliefs that guide them are true... Both forms of reasoning or inference aim to discern what is the case, and so aim, figuratively, for the mind to fit the world.

Theoretical reasoning aims to answer whether p is the case, not whether I ought to believe it, whereas practical reasoning is concerned to determine what I ought to do. The structure of theoretical reasoning is obscured if its conclusions are taken to be of the form 'I ought to believe p.' What it is best to do is that act which is better than all the alternatives, on the available reasons. But what one can or should believe is only what is genuinely worthy of belief, not what is currently better than the alternatives.

Practical reasoning aims at figuring out how to go about satisfying a desire, if opportunity permits. When one's wants or desires set a genuine end or goal, motivation to act according to the conclusion's directive is built in. It is unremarkable self-interest to attempt to satisfy one's own ends.

The objective of theoretical reasoning is to relieve doubt or to satisfy curiosity or to diminish puzzlement by achieving corresponding beliefs, whereas the objective of practical reasoning is to secure the means to realize one's ends. Because practical reasoning is directed toward action it is overtly constrained by time and resources - its objective is to discover which option is best, all available things considered. But the objective of theoretical reasoning is not merely to discover what proposition (option) is best supported by one's available evidence, but what is correct (true). Consequently, to draw a conclusion in theoretical reasoning requires the claim not just that one's evidence is the total relevant evidence available, but that the evidence is representative, rather than a skewed sample. It follows further that our limits in gathering and assessing evidence contours theoretical reasoning, but, like utilities, our limits cannot play an overt role in drawing a conclusion. You should not - and, perhaps, cannot - believe a conclusion because it is best supported by the evidence so far and that you do not have more time to examine further evidence.

One can believe, or even know, p, and p imply q, without believing or knowing q. Similarly, it can be the case that a = b and that one believes (and even knows) that a is F, without one believing that b is F, though the embedded argument is valid. So, for example, Lois Lane may know that (14) Superman flies. In the tale, it is true that (15) Superman is Clark Kent. But Lois Lane does not know (and actually believes false) that (16) Clark Kent flies.

A much-discussed example takes the problem of closure a step further, because it holds that knowledge is not closed even when the person knows the "middle" step -the relevant implication. Assume that Tony is looking at an animal behind a cage marked "zebra," which looks like a zebra. Barring any weird circumstances, we would say that Tony knows that (14) The animal I am looking at is a zebra. Let's now grant that Tony also knows the implication that (15) If the animal I am looking at is a zebra, then it is not a mule cleverly disguised to look like a zebra. (14) and (15) imply (16) The animal I am looking at is not a mule cleverly disguised to look like a zebra. Still, we are reluctant to attribute knowledge of (16) to Tony. Those who oppose closure reason that Tony has never checked that the animal he is looking at is not such a cleverly disguised mule. Tony is simply looking at the animal from outside the cage. These theorists reject: (Epistemic Closure EC) If X knows that p and X knows that p implies q, then X knows that q.

A central proposal is that belief revision should be conservative. One revises one's beliefs so that rejection or modification is minimal. You all-out believe that Skinner wrote Walden II and that Chaucer wrote the Canterbury Tales. But if you discovered that one of these is wrong, you would sooner surrender one rather than both and the latter, rather than the former, which is attested to by a greater variety of good sources. To surrender the belief about Skinner's authorship would require surrendering - nonconservatively - much more information than surrendering the latter.

Other principles of belief revision include prominently simplicity and coherence. The more a belief coheres, fits, or is explanatorily connected, with others, the more resistant it should be to modification. But some conflictual beliefs may be surrendered (in strain with conservatism) to increase coherence. You believe that ten-year-old Jim is in good health, that he will be in the tennis tournament tomorrow, and that he will meet you for lunch at noon. You learn that he is not at school today and that his mother is not at her office. You infer that Jim is sick. That best explains the latter two beliefs - unifies them in an explanatory nexus. But as a consequence you surrender other beliefs about Jim (e.g., that he will be at tennis practice later in the afternoon).

Coherence is an internal requirement on one's beliefs. But our belief corpus improves by external input, especially through our senses. The improvement is not just in the addition of new beliefs picked up as we navigate our environment. Perception and other sensory mechanisms provide for ongoing self-correction, which is a hallmark of scientific method.

Usually, of course, conclusions drawn from one's beliefs simply form new beliefs. But often conclusions are drawn that cast doubt back on the premises (beliefs) or the inferential transitions from which those conclusions are drawn. In drawing out conclusions, what rules should be used? Although in the case of induction and especially deduction a core of rules and results are well established, disputes abound about their scope and other putative rules are flat-out contested.

The vagueness of a term is that while it sorts objects into those to which the term applies and those to which it does not, it leaves undecided many objects. When a teenager's room has no clothes on the floor and dirty dishes have been removed, but it has not been dusted or swept, it is indeterminate, let's suppose, whether it is clean or not. A defender of the view that there can be true contradictions might say that the room is both clean and not clean. Others may deny the law of excluded middle: that either the room is clean or it is not clean.

A contextualist confronted by an assertion such as "John's room is clean" will respond that for everyday purposes, it is enough that his clothes are off the floor and that the dirty dishes have been removed. But if John develops asthma, you will not count the room as clean until a careful dusting is complete. The proposition expressed by the assertion is false in that context. Outside of any contextual specification, there is no assigning it a truth-value (or assigning it additional truth-values).

Most, if not all (nonartificial) terms leave undecided an unlimited range of cases for example, "blue," "happy," "short," "table," "flat," "rich," "child." At what moment does childhood end?...But is this insensitivity in the term or is it merely because of the limits of our discriminatory powers, which are foisted on to the term? "Epistemicists" favor the latter, which allows them to avoid offending against standard logic. They hold that there is an exact boundary for vague terms, but it is unknowable.

A "supervaluationist" observes that within the indeterminate cases, we are free, as far as a consistent assignment of truth-values, to decide them as serves our purposes, as contextualists claim, too...But is the supervaluationist right, to return to the earlier example, that '"either that room is clean or not" is definitely true, when the room is clearly a borderline case? Worries like this incline others, although far fewer, to take the route of treating the initial reaction that neither alternative is true at face value. We can say only that John's room is clean to a certain degree, or to a higher degree than others. The error on this probabilistic approach is to contrive to derive absolute judgments from matters of degree.

Although it seems evident that positive inductive evidence for a hypothesis provides support for it, does that support actually provide reasons to believe that its claims will continue to hold (in the future)? A negative answer was offered by Hume, at the launching point for investigations of induction. Hume writes: "We have said, that all arguments concerning existence are founded on the relation of cause and effect; that our knowledge of that relation is derived entirely from experience; and that all our experimental conclusions proceed upon the supposition, that the future will be conformable to the past. To endeavour, therefore, the proof of this last supposition by probable arguments, or arguments regarding existence, must be evidently going in a circle, and taking that for granted, which is the very point in question."

Nondemonstrative arguments about an unobserved (future) event only work if we assume that "the future will be conformable to the past," which is referred to as the assumption of the uniformity of nature (UN) - the future will be like the past (at least in respect of the regularity involved)...The cogency of this argument turns on the uniformity supposition. Its defense can not be, again, by demonstrative argument, because it is possible that the future is not like the past in this or any other respect. The laws could break down. ("It's possible," in Hume's weak sense of possibility as logical consistency, that the sun does not rise tomorrow.)

But the premise affirmed is effectively the conclusion itself or a proposition that implies it. The reasoning is circular in a way that would be found for any inductive or nondemonstrative argument, since they all require the uniformity assumption. In brief, even if induction has worked in the past to infer that it will continue to work in the future would itself presuppose the validity of inductive inference, which is what we were supposed to prove.

We know that overwhelmingly inductive inferences do work. They must or else our success in action, and that of other animals, makes no sense, since induction is our guide to forming expectations and to the future. This is not an answer to Hume's sceptical argument, but only a way to clarify its scope. Even if we cannot demonstrate that inductive arguments must be reliable, it is enough for our confidence in induction that it regularly succeeds. The possibility that the future is unlike the past is not often realized and the world is by-and-large lawful, even if neither observation can be massaged into a justification of induction.

A natural form of inference is to infer the hypothesis that best explains the data. Sherlock Holmes infers that the owner of the dog committed the crime because this is the best explanation of why the dog did not bark when the crime was committed nearby. The data of the dog's not barking confirms the hypothesis that the owner committed the crime, and the hypothesis is introduced to explain why the dog did not bark. Inference and explanation implicate each other. Inference to the best explanation is at work where observable events, like John's rude behavior at a party, are explained by the hypothesis of an unobserved (and sometimes unobservable) cause (e.g., John was just fired from his job).

Inference to the best explanation captures Peirce's "abduction," whereby plausibility accrues to a hypothesis - it is worth taking seriously. When you meet someone at a party who dresses in a similar slightly off-beat way of another acquaintance, you might think that they share political or cultural views. Although the off-beat dress is a reason to take seriously the hypothesis that the two share political or cultural views, it is hardly much of a reason to actually believe it. Suggestive or analogical reasons are important in view of the underdetermination problem of the unlimited number of hypotheses to fit any data, as well as the problem of coming up with credible hypotheses to explain complex data or observations.

If the best explanation is accepted as correct or even as worthy of investigation, it must at least provide a good explanation, not merely the best of a lousy lot. Criteria for the best explanation include that the hypothesis is simple, conservative, and unifying. However, the criteria should not include an explicitly truth relevant property such as high probability. That is the conclusion to be reached not assumed. The hypothesis that yields the most understanding must prove itself to be the likeliest.

Strict empiricists - stricter even than Hume - are not satisfied with the claimed power of reflection. They attempt a straightforward a posteriori or inductive approach to logical laws as generalizations from observations of uniformly successful inferences. These laws are subject to hypothesis testing akin to any empirical claim.

The strict empiricist approach is unpopular on Kantian grounds that observations or related evidential considerations can never establish the necessity of logical laws. An improvement over empiricism on this count is that with a logical law we cannot conceive of its failing. But what is the relation between conceivability or imaginability and real possibility? As Putnam noted, our ability to conceive that water is not H2O does not entail that it is really possible that water is not H2O.

Goodman explicitly compared the justification of inductive and deductive rules: "How do we justify a deduction? Plainly, by showing that it conforms to the general rules of deductive inference.... Analogously, the basic task in justifying an inductive inference is to show that it conforms to the general rules of induction.... Principles of deductive inference are justified by their conformity with accepted deductive practice.... Justification of general rules thus derives from judgments rejecting or accepting particular deductive inferences. This looks flagrantly circular.... But this circle is a virtuous one. The point is that rules and particular inferences alike are justified by being brought into agreement with each other. A rule is amended if it yields an inference we are unwilling to accept; an inference is rejected if it violates a rule we are unwilling to amend. The process of justification is the delicate one of making mutual adjustments between rules and accepted inferences; and in the agreement achieved lies the only justification needed for either."

Reflective equilibrium is intended as an alternative to a purely a priori justification of logical principles. Reflective equilibrium embraces neither a crude inductive justification (as just a generalization from successful instances) nor a "foundational" one, which treats some principles as sacrosanct.

In this respect, reflective equilibrium is closely aligned with coherentism in epistemology, the view that justification is holistic: A principle is justified to the extent that it coheres within one's corpus of beliefs. However, if the coherence is only within one's current corpus of beliefs, it is a narrow reflective equilibrium. It lacks the justificatory force of a wide reflective equilibrium, where one's judgments (intuitions) and principles are evaluated against alternatives principles and they are subjected to extended critical analysis. Although the approach was originally proposed as a guide to generating inductive rules, it has been invoked predominantly as the underlying model for theory construction in moral or political philosophy.... However, reflective equilibrium can provide little further substantive guidance. It does not specify how to balance among principles or judgments when they conflict. So it cannot settle serious disputes.

Paradoxes involve the derivation of either a contradictory or a starkly unacceptable conclusion, like that there are no heaps or rich people, from prima facie valid chains of reasoning, derived from apparently sound premises. A solution to a paradox would be to uncover an error either in the premises or in the reasoning.

Much of our reasoning and particularly our ordinary arguments are tacit or implicit as compared to the reconstructions of those arguments, where missing or hidden assumptions are stated... This observation provides no formula for eliminating common fallacies, because ordinary argument and reasoning cannot aspire to much explicitness. Implicitness is a barrier that can be overcome in specific cases, but it is ineliminable, for reasons of economy and limited grasp of our beliefs. Tacitness or implicitness is evident in the drawing of conversational implicatures, allowing communication of much information with brevity.

Despite the essential benefits to reasoning of implicitness, the reconstruction of arguments in which assumptions are stated and terms and statements are standardized is central for purposes of the critical analysis of arguments. By rendering these assumptions visible and as entering claims to truth, burdens of proof are imposed on the claimant. Explicitness renders bad reasoning and confabulation more difficult. Explicitization is a natural consequence of argumentation as a dialectical exchange. Because argumentation is social - ideally, public - to engage in it is to impose a questioner or critic or interlocutor on oneself, and so a device of selfcorrection. If the interlocutor is not under the arguer's control, if he does not share the same biases as the arguer, he is thereby an obstacle to bending argument to favor the arguer's own position. Socratic questioning compels focus by interlocutors on crucial consequences or implications, keeping the dialectical exchange on target. Of course, explicitization can also add biased information. It can overload and distract one's thoughts. Interlocutors may be heavily selfselected. But these are interferences with argumentation, and our purpose here is to highlight its potential value functioning optimally for reasoning.

Argumentation involves moving one's argument from its inchoate form to an articulate one. For complex arguments, argumentation almost certainly calls for written formulation, which is characterized by greater explicitness, since addressed to a more impersonal audience (than in casual thought or conversation). In articulate forms, the social activity of argumentation can become public, with unrestricted access. In argumentation, participants attempt to render explicit implicit assumptions, inferences, qualifications, and so on. Explicitization brings forth the basic structures or generalizations that constitute the underlying -warrants for inferences.

Inductive Logic and Inductive Reasoning, H. Kyburg

One very narrow and very specific meaning is that inductive inference is the inference from a set of observations or observation sentences (crow #1 is black; crow #2 is black;...; crow #n is black) to their universal generalization (all crows are black). There is not much logic here, but there is a big problem: to determine when, if ever, such an inference is "justified." A somewhat less ambitious construal of "induction" is as the inference from a statistical sample to a statistical generalization, or an approximate statistical generalization: from "51% of the first 10,000 tosses of this coin yielded heads," to "Roughly half of the tosses of the coin will, in the long run, yield heads." So construed, the line between the logic of induction and the mathematics of statistics is a bit vague. This has been of little help to inductive logic, since the logic of statisti- K cal inference has itself been controversial. Another way of looking at induction is as a part of logic proper. This approach takes as its guiding insight that while in the case of valid deductive inference every model of the premises is a model of the conclusion, in the case of valid inductive inference we should ask that most of the models of the premises (the statements expressing the evidence) are models of the conclusion. The problem, of course, is how to count models in any reasonably complex language. There are an infinite number of ways of constructing models of even quite simple languages.

In the past, many writers, recognizing that the conclusion of an inductive inference is generally not certain, have focused on the idea that the conclusion of an inductive inference may yet be probable. This is helpful only if we understand probability, and probability itself has been controversial; several different interpretations of probability have been offered, not all of which are of relevance to induction. As a branch of mathematics, there is nothing mysterious about probability. Probability is defined on an algebra of sets', it is nonnegative with a maximum value of 1; and it is additive, which just means that if A and B are disjoint sets, the probability of their union is the sum of their probabilities. But this is not what we want to know. We want to know what those sets are for which probability is defined. We want to know where the values of those probabilities come from. We want to know how these matters are related to knowledge or rational belief. In short, we want to how probability fits into logic, and to explore that question we need to reflect on the foundations of logic itself.

Logic is not the theory of how we do reason, but the theory of how we ought to reason. But this seems almost as silly as the descriptive claim would be: surely it is not intended that we should reason in accord with some particular system of logic! We are not being exhorted to construct proofs in our minds, that is sequences of formulas each of which is either a premise or is inferred from earlier formulas by a permissible rule of inference. (And if that were the case, which formal system would we be supposed to follow?)

In relatively recent years (the last twenty or twenty-five) we have seen the introduction of nonmonotonic logics and probabilistic logics. These are often intended to play the role of inductive logic.

In short, even if we could settle on one of these formalisms as the right way to approach nonmonotonic logic, there seem to be insuperable difficulties lying in the way of applying it to anything more than the simplest toy Tweety model. There is the problem of representing the evidence in such a way that it can be agreed to (or argued over); and, even more serious in the light of the difficulty with the evidence, there is the question of how the system can both be interpreted in terms of representation and normativity. How do we resolve the tension between what people actually do, what people think it is intuitively correct to do, and what people really ought to do?

Another approach to uncertain inference that has been getting a lot of press in recent years is Probabilism. I wouldn't presume to define probabilism - I'm not even sure it should be capitalized - but the basic idea is that we replace qualitative all-or-none belief by degrees of belief, and we are to modify our degrees of belief in the light of new evidence by conditioning on that evidence. This approach is called "Probabilism" because degrees of belief are to satisfy the probability axioms, and conditioning is to satisfy the relation imposed by the condition that the degree of belief in a conjunction is to be the product of the degree of belief in one conjunct multiplied by the conditional degree of belief in the other conjunct, given the first conjunct.

Representation is anyway only part of the story. If logic is to be a theory of what follows from what, or of what is evidence for what, then we must develop a standard, a criterion, and we must also develop a means of applying it. In the first order deductive realm, we must adopt a classical, or an intuitionistic, or a minimalist standard; and we must also develop a way of knowing when that standard is met. There are two things that this can mean: We might ask for a decision procedure: given a set of formulas and a formula, this would be a procedure that would tell us if the formula followed from the set of formulas.

One difficulty we face in the case of inductive argument is that the set of sentences that yields our conclusion must be very large - it must comprise everything we know. This is a burden for nonmonotonic logic as well as for inductive logic. In both cases, we must allow that a conclusion S is supported by a set of evidence statements £, but is not supported by a more inclusive set rt evidence statements £'. Both probabilists and logicians fudge this problem: the former write B for "background knowledge," the latter write "F" for the set of accepted facts. It is easy to write B or F to stand for the evidence, but if we are either to represent realistic idealizations or apply the theory normatively, we need some way of unpacking the contents of £.

The most important difference [between inductive and deductive arguments] is that while a deductive argument depends on an explicit (usually short) list of premises, an inductive argument depends on "all" our background knowledge. This is a consequence of the nonmonotonicity of inductive argument; new information can always undermine an inductive conclusion. As a consequence, the background knowledge B or the facts F do not easily admit of explicit listing, as do the premises of a deductive argument. But we must be able to say something about what is there. Another significant difference is that there is nothing corresponding to "proof for inductive arguments.

Just as modus ponens may be taken as the sole form of deductive inference, so direct inference may be taken as the sole form of inductive inference. Direct inference is the form of inference that proceeds from knowledge of relative frequency, and of membership in a reference class, to probability. For example, if you know that about a third of the freshman women are anorexic, and that Jane is a freshman woman, then there is an argument that the probability that Jane is anorexic is about a third. Of course there are other considerations. Jane is a college woman, and maybe you know that only between 10 percent and 14 percent of college women are anorexic. For that matter, you may know Jane personally, and know that she is fat and jolly.

Direct inference is unlike modus ponens, however, since the probability to which it leads is only a possible conclusion. As in the example, many of these conclusions may conflict. We face the problem of sorting out and combining the various possible inferences.

The idea we take as basic for inductive logic is that we can inductively infer S from £ just in case the chance of our being in error is less than e. We seek truth, else we would not infer at all; but we also seek to control error. We cannot ensure the truth of our inferences; we can ensure that errors are rare...But can this be made to work? Can we show that in a state of empirical ignorance, empirical data can render statistical generalizations highly probable? The answer is "yes."

If inductive conclusions are to be accepted, as we suggest, however, we must immediately face the question of how a rejection level e is to be chosen. But this is a question that is faced by researchers all the time, and is answered, somewhat arbitrarily, by the conventions of the trade. Psychologists are often willing to reject null hypotheses at the 0.05 or 0.02 level; in the physical sciences one supposes that measurements are not more than two and a half standard deviations in error. Engineers deal with factors of safety of two to ten, which can also be translated into probabilities of error.

Inductive logic is not "inductive" because it reflects how people think, but because it concerns what is evidence for what, just as deductive logic concerns what follows from what. But there is one big difference between deductive logic and inductive logic. If there is a proof that C follows from PI , . . . , Pn it can ordinarily be rendered short and perspicuous. Such a proof depends only on the sentences PI , . . . , Pn. In contrast, when we say that P\ . . . , Pn provides evidence for C, citing Fj , . . . , Pn explicitly, we mean that it does so in the context of everything else we know, £. Since an addition to our total evidence £ can undermine the relation of evidence, the evidential relation depends on what we don't know as well as on what we know, or, put otherwise, in depends on all we know. That is why the inductive evidential relation is nonmonotonic, while the entailment relation is not.

The difficulty in inductive logic is caused by the fact that the "premises" of an inductive argument consist of everything we know, and, more seriously, on the fact that an inductive argument depends on entailments of what we know. The biggest problem is managing £. Earlier I pointed out that writing "B" for background knowledge doesn't help us in resolving disagreements about what is evidence for what. Writing "£" is no more help. What we need to do is to represent £ explicitly. Of course you can't "write down everything you know." But in a scientific context, by and large, most of what differentiates your body of knowledge from mine is irrelevant to the support provided C by PI , . . . , Pn. It does not seem unreasonable to ask that a basis for £ be provided. Furthermore, inductive support is measured by evidential probability, and all probabilities come from constructions of direct inference.

Reasoning, Decision Making, and Rationality, J. Evans, D. Over, K. Manktelow

It is clear that both reasoning and decision tasks involve high-level thought processes. On further reflection it is apparent that reasoning tasks usually involve making decisions, and that choosing between actions often requires one to make inferences. In real-world situations the distinction between reasoning and decision making is blurred.

Decision making, or at least rational decision making, usually involves forecasting. That is to say, one action is preferred to another because the chooser believes that he or she would rather live in the slightly different world that will exist when this action is taken. But what does forecasting consist of, if not reasoning? Consider the situation of a school leaver deciding which university to apply to for degree study. A number of factors will influence such a decision, including the academic merits of the courses offered and the advantages and disadvantages of different geographical locations. In reading prospectuses of different universities the chooser is trying to infer which course he or she will most benefit from. The sophisticated chooser will make allowances for the promotional techniques and biases in the literature read - this too is reasoning.

It is difficult to think of cases in the real world when we make inferences except to make a decision or achieve a goal of some kind. The apparent exception is that of inferences drawn in order to enhance our knowledge or revise our beliefs in some way. However, maintenance of coherent and accurate belief systems is fundamental to our survival and achievement of goals in the real world and is clearly motivated in its own right. Hence some of our goals are epistemic or knowledge serving.

Evans has argued that the debate about rationality in human reasoning and decision making is confused by two different, but implicit definitions of rationality. These can be defined as follows: rationality1 (rationality of purpose): reasoning in a way which helps one to achieve one's goals; rationality2 (rationality of process): reasoning in a way which conforms to a supposedly appropriate normative system such as formal logic.

In the classical decision-making literature the primary definition of rationality has been an idealized version of rationality1: A rational person is believed to be one who chooses in such a way as to maximize his or her SEU....In the literature on deductive reasoning, however, the rationality argument has focused on the concept of logicality, that is, validity or deductive correctness in reasoning, with the consequent adoption of the rationality2 concept. There is, of course, a further implicit assumption, namely that rationality2 serves rationality1: in particular that logical reasoning will lead to the achievement of goals.

We assume that people try to achieve goals, and when they fail it is indicative of limitations in their processing capacity or ability. Due to cognitive limitations we also propose that goals are more likely to be achieved by satisficing, that is, finding an adequate solution, rather than by optimizing or maximizing utility across all possible choices and outcomes as proposed in classical decision theory.

Recently, there has been increasing interest in a type of thinking in which the relation between reasoning and decision making, and between rationality1 and rationality2, has been brought into sharp focus. This is the type actually known in philosophy as practical reasoning, and distinguished from so-called theoretical reasoning, the center of so much earlier psychological research. People use practical reasoning to try to achieve their goals in the actions they perform, and when they do this in the right way, they display rationality1. They use so-called theoretical reasoning to try to acquire true beliefs about matters of fact, and they have rationality2 when they do this in the right way.

It is our purpose in this paper to concentrate on rationality1 and practical reasoning. Before doing so, however, a little more must be said about the nature of rationality2 and theoretical reasoning. We concede that the literature on deductive reasoning does contain evidence of deductive competence and that is one aspect of the evidence that theories of reasoning must explain. However, we also believe that an undue emphasis on rationality2 and the belief in the logicality = rationality equation has not only dominated theoretical effort in the psychology of reasoning but has also led to widespread misinterpretation of much of the data which demonstrate "biases" and content effects.

Rational1 reasoning in the real world means that it is applied to the achievement of a practical goal, or the selection of a decision, and that as much relevant knowledge as possible is retrieved and applied to the problem at hand. It is in this context that laboratory studies must be interpreted. If logical errors occur then we must ask first whether these result from processes which would be adaptive (i.e., goalfulfilling) in application to real-world problems. Only if the answer to this is negative is it sensible to consider what the "errors" tell us about the cognitive constraints on human inference.

It is possible to construct four classes of syllogism: valid-believable, validunbelievable, invalid-believable, and invalidunbelievable. In spite of the use of explicit deductive reasoning instructions and an intelligent undergraduate student population, massive effects of belief bias were observed. The basic acceptance rate of conclusions in these four categories observed by Evans et al. is shown in Table 1. There are three substantial and highly significant effects: (1) Subjects endorse more conclusions which are logically valid than invalid; (2) subjects endorse more conclusions which are believable than unbelievable; and (3) logic and belief interact in their effect on subjects' choices. The latter finding reflects the fact that the belief bias effect is much larger for invalid syllogisms.

Despite the fact that subjects can figure out the logic - as the large effect of validity shows - they were nonetheless quite unable to ignore the believability of the conclusions. Can the belief bias effect be explained within the notion of bounded rationality1 presented earlier? We believe it can. First, we have to recognize that mechanisms of reasoning have evolved to facilitate the achievement of goals in the real world rather than to solve problems in the psychological laboratory. Second, we have to be sensitive to relevant cognitive constraints. The first question, then, is whether belief bias effects could result from a normally adaptive process. Both major theoretical accounts considered above involve the notion of selective scrutiny. Only conclusions which are unbelievable to the reasoner appear likely to get a full process of logical evaluation. Other invalid conclusions are often accepted unless they are incompatible with the premises or unless elaborated instructions are provided. In general, both believable and even neutral conclusions tend to be accepted without adequate search for counter-examples.

Why would it be adaptive to reason only selectively and more so when the argument goes against rather than for one's beliefs? The maintenance of a large and stable set of beliefs is essential for intelligent behavior, since this forms the basis for any actions which one may take to achieve one's goals. When arguments are encountered which support existing beliefs, the evidence suggests that we do not examine them closely. This is surely rational1 since (1) it is advantageous to maintain beliefs unless there is good reason to revise them, and (2) the processing effort required constantly to question the evidence of current beliefs would be enormous. The situation when confronted with argument or evidence for a statement which contradicts one's beliefs is quite different. To accept such an argument uncritically would be damaging to the individual since this would introduce a contradiction and disrupt the internal consistency of their belief system. Hence, it is quite rational that such arguments should be subjected to the closest possible scrutiny and refuted if at all possible.

The primary purpose of most of our ordinary reasoning is to help us make good decisions, so that we can have reasonable success in achieving our goals. This point was brought out clearly by Grice, who noted that efficient communication has to be a goal-directed process, in which the participants must infer each other's purposes and then make appropriate decisions about their own speech acts and other actions. Similarly, the purpose of reasoning is best served by drawing inferences from all our beliefs, not just from an artificially restricted set of premises, as in most psychological experiments on reasoning.

On this basis, we should also expect people to display rationality1 in experiments calling for something like ordinary practical reasoning, which is aimed at realistic goals and not at abstract theoretical ones. Striking results of changing the nature of experimental reasoning tasks in this way can be observed in the recent history of work on the Wason selection task. The developments in question have focused selection task research on a type of deontic reasoning which is directly and immediately practical. The object of deontic reasoning is to infer what actions ought to be taken, or may be taken, and it calls for cognitions of probability, utility, and social perspective - aspects of thought which hitherto were the prime concern of research on decision making. Thus in deonticreasoning research we have a premier case of cross-pollination between the two fields of reasoning and decision making.

As Light et al. put it, responses in deontic selection tasks should be judged as correct if they lead to the detection of the possible violators, independent of the values that the corresponding cases would have under a formal heading. Detecting violation is an important practical matter. If we could not do this, we would fail to achieve many of our prudential, social, and moral goals.

There is, in fact, already some evidence that subjects do far less well in a deontic selection task when violating a rule would bring less benefit than conforming to it, rather than a strict loss from a neutral position, such as might result from being punished by an authority. Classical normative decision theory does not distinguish between benefits and costs in a way which would justify this. Some descriptive decision theories, however, do predict special sensitivity to costs, such as the seminal prospect theory of Kahneman and Tversky with its notion of a reference point, below which one thinks of oneself as suffering a loss. It can also be argued that, if one's present position is reasonably satisfactory, then being especially sensitive to possible losses is a good, rational1, satisficing strategy.

Depending on the circumstances, we might be able to set a reasonable standard for the number and type of deontic inferences people can be expected to perform, if they have rationality1. We could not necessarily require them to perform all relevant deontic inferences, from the rules they accept, and so maximize their subjective expected utility, where this is defined by the ideal preferences they would have if they had the time and mental power to perform all these inferences. This is just to say that we could only require some degree of bounded rationality1 of them.

Research so far conducted has not shown that there is a widespread tendency to violate the principal principle in ordinary decision making, nor that when it is sometimes violated there, people invariably fail to achieve their goals as a result. Sometimes being overconfident in the technical sense could help to achieve one's goals, by increasing selfconfidence in the ordinary sense and keeping doubts from one's mind. A woman who is overconfident about herself having a healthy baby, even though she knows the objective frequency of complications in pregnancy, may be helped by her positive attitude. Griffin and Tversky rightly give examples in which overconfidence is more of a cost than a benefit, but then we would not claim that people are never irrationali in particular cases, as there are cognitive constraints to take into account. These can exist alongside a general tendency for human beings to achieve a reasonable number of their goals, which they would have to do to survive any length of time, let alone to create complex societies and advanced technologies.

In fact, people sometimes achieve a goal in part because they do not try to maximize utility (in the technical sense) or hold coherent and consistent beliefs. With bounded capacities and limited time, people would sometimes miss the chance to achieve a reasonably satisfying goal if they paused to wonder whether their preference relation or their beliefs satisfied abstract normative principles. They can sometimes save precious time by accepting a plausible conclusion without examining closely the logic of its argument, or by being very vague about their preferences.

Causal Thinking, L. Rips

We remember causes and effects for event types as well as for event tokens. Ramming heavy objects into more fragile ones typically causes the fragile items damage; repeating phone numbers four or five times typically causes us to remember them for awhile. Negotiating routine events, constructing explanations, and making predictions all require memory for causal relations among event categories. Causal generalities underlie our concepts of natural kinds, like daisies and diamonds and support our concepts of artifacts like pianos or prisms. Our knowledge of how beliefs and desires cause actions in other people props up our own social activities.

Causality is an inherently abstract relation - one that holds not only between moving physical objects but also between subatomic particles, galaxies, and lots in the middle - and this abstractness makes it difficult to come up with a plausible theory that would have us perceiving it directly, as opposed to inferring it from more concrete perceived information. There's no clear way to defeat the idea that "when we consider these objects with the utmost attention, we find only that the one body approaches the other; and the motion of it precedes that of the other without any sensible interval".

Some causal judgments depend vitally on detailed perceptual processing, while others depend more heavily on schemas, rules, probabilities, and other higher-order factors. What's not so clear is whether the dissociations also clinch the case for a perceptual causality detector. The right hemispheres of Roser et al.'s split-brain patients could assess the quality of launching events even though they were unable to evaluate the impact of statistical independencies. But this leaves a lot of room for the influence of other sorts of inference or association on judgments about launching. Suppose, for example, that launching judgments depend on whether observers are reminded of real-world interactions of similar objects. Unless the right hemisphere is unable to process these reminders, inference could still influence decisions about launchings. Similarly, Schlottmann and Shanks's finding shows that observers can ignore long-run probabilities in assessing the convincingness of a particular collision, but not that they ignore prior knowledge of analogous physical interactions.

Even if we can literally perceive causality in some situations, we have to resort to indirect methods in others. A careful look at a CD player's innards can't disclose the causal link between the reflected pattern of light and the transmission of sound signals. We may see the reflected light and hear the resulting sound, but we don't have perceptual access to the connection between them. Similarly, we can't see atmospheric pressure influencing the boiling point of a liquid or a virus producing a flu symptom or other people's beliefs motivating their actions. Experiments in science would be unnecessary if all we had to do to isolate a causal mechanism is look.

We can sometimes rely on experts to tell us about the hidden causes. Allergists are often good on allergies, botanists on plants, and Miss Manners on manners. But sometimes we have to proceed on our own, and the question is how ordinary people cope with the task of recognizing causal relationships when they can't look them up. The answer that psychologists have usually given to this question is that people operate from bottom up, observing the temporal co-occurrence of events and making an inductive inference to a causal connection. They might passively register the presence or absence of a potential cause and its effects or they may actively intervene, pressing some buttons to see what happens. In either case, they decide whether a cause-effect link is present on the basis of these results.

If we suspect event type C causes event type E, we should expect to find E present when C is present and E absent when C is absent. This correlation might not be inevitable even if C really is a cause of E. Perhaps E has an alternative cause C'; so E could appear without C. Or perhaps C is only a contributing cause, requiring C" in order to produce E; then C could appear without E. But if we can sidestep these possibilities or are willing to define cause in a way that eliminates them, then a correlation between C and E may provide evidence of a causal relation. Codifying this idea, Mill proposed a series of wellknown rules or canons for isolating the cause (or effect) of a phenomenon. The best known of these canons are the method of agreement and the method of difference. Suppose you're looking for the cause of event type E. To proceed by the method of agreement, you should find a set of situations in which E occurs. If cause C also occurs in all these situations but no other potential cause does, then C causes E. To use the method of difference, which Mill regarded as more definitive, you should find two situations that hold constant all but one potential cause, C, of E. If E is present when C is present, and E is absent when C is absent, then C causes E.

Creatures learning that, say, a shock often follows a tone are remembering contingency information about the tone and shock (or the pain or fear that the shock creates - sorry, animal lovers, but these aren't my experiments). A number of researchers have proposed that this primitive form of association might provide the basis for humans' causal judgments... In particular, the associative strength between a specific cue (e.g., tone) and an unconditioned stimulus (shock) depends on the associative strength of other cues (lights, shapes, colors, etc.) that happen to be in play. The associative strength for a particular cue is smaller, for example, if the environment already contains stronger cues for the same effect.

Although a single contrast or correlation between factors may not be convincing evidence, multiple correlations may sometimes reveal more about the causal set up....There are limits to these methods, however, that are similar to those we noted in connection with single correlations. In the first place, there may still be confounding causes that are not among the factors considered in the analysis.

To compound these difficulties for the bottom-up, correlation-to-causation approach, the causal environment typically contains an enormous number of factors that could produce a given effect.

Since there is no end to the possibilities, there is no way to determine for each of them whether it is the cause, making a purely bottom-up approach completely hopeless. We should again distinguish the plight of the scientist from the task of describing laypeople's causal search. Laypeople may take into account only a handful of potential causes and test each for a correlation with the effect. Although such a procedure might not be normatively correct, it may nevertheless be the recipe people follow in everyday life. But even if people use correlations over a restricted set of factors, an explanation of their causal reasoning would then also have to include an account at how they arrive at the restricted set. The factors they test are the factors they attend to, of course, but what determines what they attend to? People's causal thinking often aims at explaining some phenomenon, where what needs explaining may be a function of what seems unusual or abnormal within a specific context. The explanation process itself depends on broadly pragmatic factors, such as the explainers' interest or point of view, the contrast class of explanations they have in mind, the intended audience for the explanation, and the availability of evidence, among others. The same goes for determining "the cause" of a phenomenon, which is a disguised way of asking for the main cause or most important cause.

Tversky and Kahneman's experiments on causal schemas show that causal theories can dictate estimates of conditional probabilities. Participants in one experiment were asked to choose among the following options: Which of the following events is more probable? [a] That a girl has blue eyes if her mother has blue eyes. (b) That a mother has blue eyes if her daughter has blue eyes. (c) The two events are equally probable. The converse conditional probabilities in (a] and [b] are necessarily equal, according to Bayes Theorem, provided that the (marginal or unconditional) probability of being a blue-eyed mother is the same as being a blue-eyed daughter. (A follow-up experiment verified that most participants think this equality holds.) The results showed that 45 percent of participants correctly chose option (c). The remaining participants, however, chose (a) much more often than (b): 42 percent versus 13 percent. According to Tversky and Kahneman's interpretation, these judgments are biased by the belief that it's the mother who is causally responsible for the daughter's eye color rather than the reverse. This causal asymmetry induces an incorrect impression of an asymmetry in the conditional probabilities.

We've just looked at the possibility that people discover causal relations by noticing the patterning of events in their surroundings. That method is problematic for both theoretical and empirical reasons. Theoretically, there is no limit on the number or complexity of potential causal relationships, and correlation is often unable to decide among these rival causal set ups. Empirically, there is no compelling evidence that people have hard-wired cause detectors, so people probably don't automatically derive causal facts from event perception. Moreover, our ability to infer cause from event co-occurrence seems to rely heavily on higher-level beliefs about what sorts of events can cause others, on beliefs about how events interact mechanistically, and on pragmatic pressures concerning what needs to be explained. To make matters worse, knowledge about cause sometimes colors our knowledge about co-occurrence frequency or correlation.

The classic alternative strategy for deriving causal knowledge is a form of inference to the best explanation. We can start with theories about the potential causes of some phenomenon and then check to see which theory best predicts the data. The theory that provides the best fit is the one that gives the right causal picture. Of course, this form of inference doesn't give us certainty about our causal conclusions, since it depends on the range of alternatives we've considered, on the validity of the tests we've performed, and on the goodness of the data we've collected. But no method yields certainty about such matters. What could give us a better idea about correct causal relations than the best explanation that exploits them? This approach reserves a place for observational data, but the place is at the receiving end of a causal theory rather than at its source. This top-down strategy, however, yields a host of further psychological problems. We still need to know the source of our theories or hypotheses if they don't arise purely from observation. We also need to consider how people use causal theories to make the sorts of predictions that hypothesis testing depends on. In this last respect, the causal schemas or Bayes nets that we looked at earlier can be helpful. We noted that people don't always accurately construct such schemes from data, even when they're allowed to manipulate relevant variables. Nevertheless, once people settle on such a representation, it may guide them to conclusions that correctly follow.

According to one top-down theory of causality, we have, perhaps innately, certain primitive causal concepts or principles that we bring to bear on the events we observe or talk about, primitives that lend the events a causal interpretation. Perhaps there is a single primitive causal relation, cause(x, y), that we combine with other concepts to produce more complex and specific causal descriptions....Or perhaps there are several primitive causal relations or subtypes that vary in ways that distinguish among causing, enabling, and preventing, among others.

The phrase causal reasoning could potentially apply to nearly any type of causal thinking, including the types of causal attribution that we considered in the first part of this chapter. The issue there was how we reason to causal beliefs from data or other noncausal sources. Our considerations so far suggest that there may be relatively little reliable reasoning of this sort without a healthy dose of top-down causal information already in place. But how well are we able to exploit this top-down information? Once we know a batch of causal relations, how do we use them in drawing further conclusions?

Thompson compared arguments like the ones in (9) to see how likely her participants were to say that the conclusion logically followed: (9) a. If butter is heated, then it melts. The butter has melted. Was the butter heated? b. If the car is out of gas, then it stalls. The car has stalled. Is the car out of gas? Arguments (9a) and (9b) share the same form in that both have the structure: Jfp then q; q; p? So if participants attend only to this form in deciding about the arguments, they should respond in the same way to each. However, people's beliefs about cars include the fact that running out of gas is just one thing that could cause a car to stall, whereas their beliefs about butter include the fact that heating butter is virtually the only way to get it to melt. If people lean on these beliefs in determining whether the conclusions logically follow, they should be more likely to endorse the argument in (9a) than the one in (9b), and indeed they do. The difference in acceptance rates is about forty percentage points. It is possible to argue about the role played by causal information versus more abstract logical information in experiments like these, and other aspects of the data show that participants aren't simply throwing away the i f . . . then format in favor of their causal beliefs.

Thompson and others view these results as due to people's knowledge of necessary and sufficient conditions. Heating butter is both necessary and sufficient for its melting, whereas running out of gas is sufficient but not necessary for a car stalling. Thus, given that the butter was melted, it was probably heated; but given the car has stalled, it may not be out of gas. The same point is sometimes made in terms of "alternative" causes or "additional" causes. An alternative cause is one that, independently of the stated cause (e.g., running out of gas), is able to bring about the effect, and an additional cause is one that must be conjoined with the stated cause in order for the effect to occur. The explanation of the difference between (9a) and (9b) is therefore that participants know of no alternative causes for the conditional in (9a) that would block the inference, but they do know of alternatives for the conditional in (9b) - perhaps an overheated engine or a broken fuel pump. Giving participants further premises or reminders that explicitly mention alternative or additional causes also affects the conclusions they're willing to draw.

Causal theorizing must be essential, both in everyday thinking and scientific endeavors, but it is unclear how people accomplish it. The implication of the first part of this paper is that we probably don't do such thinking by strictly bottom-up observation. We can interpret simple displays of colliding geometric shapes as instances of pushings, pullings, and other causal events. Similarly, we can interpret other swarming movements of geometrical shapes as instances of actions - for example, chasings, catchings, and fightings, as Heider and Simmel demonstrated. But we can also take a more analytical attitude to these displays, interpreting these movements as no more than approachings, touchings, and departings with no implication that one shape caused the other to move. There is no evidence to suggest that the causal interpretations are hardwired or impenetrable in the way standard perceptual illusions often are. The evidence is consistent with the idea that we see these demos as causal, but probably only in the way that we see certain visual arrays as cows or toasters. This suggestion is reinforced by the fact that, although sevenmonth- old infants may register some of these animations as special, others that adults report as causal are not distinctive for these infants. Of course, doubts about innate perceptual causality detectors needn't extend to doubts about innate causal concepts, but it seems likely that causal concepts, innate or learned, must have sources that aren't purely perceptual.

Are the sources of causality co-occurrence frequencies? Here there are both empirical and conceptual difficulties. On the empirical side, people are obviously limited in which potential causes they can test using frequency-based methods, and there is no theory of how they search through the space of these causes. Moreover, even when an experimenter tells participants about the relevant candidates and provides the relevant frequencies, the participants appear guided by prior hypotheses in their evaluation of the data.

The empirical results are generally in line with the conclusions of Waldmann and others that people pursue knowledge of cause in a largely top-down fashion. The theoretical results are in line with the conclusion that this might be the correct way for them to pursue it. A top-down approach implies that people begin with hypotheses when they assess or reason about cause. But this leaves plenty of room for variation. Causal hypotheses could be anything from fragmented bits of information about a system to highly integrated and consistent theories. It's clear that people can reason with causal information and that this reasoning differs (sometimes appropriately) from what they do with similar indicative conditionals. It also seems likely that people's causal knowledge of a situation is not entirely isolated into units at the grain of individual atomic propositions. It is very unclear, though, what else we can say about such representations.

To accord with the facts about human causal thinking, we need a representation that's less nerdy - less tied to statistical dependencies and more discursive. This doesn't mean that we should jettison Bayes nets' insights, especially insights into the differences between intervention and observation. But it does suggest that we should be looking for a representation that better highlights people's talents in describing and reasoning about causation and downplays ties to purely quantitative phenomena.