The need to explain

How do reasoners deal with inconsistencies? James (1907) believed that the rational solution is to revise your beliefs and to do so in a minimal way. We propose an alternative: You explain the origins of an inconsistency, which has the side effect of a revision to your beliefs. This hypothesis predicts that individuals should spontaneously create explanations of inconsistencies rather than refute one of the assertions and that they should rate explanations as more probable than refutations. A pilot study showed that participants spontaneously explain inconsistencies when they are asked what follows from inconsistent premises. In three subsequent experiments, participants were asked to compare explanations of inconsistencies against minimal refutations of the inconsistent premises. In Experiment 1, participants chose which conclusion was most probable; in Experiment 2 they rank ordered the conclusions based on their probability; and in Experiment 3 they estimated the mean probability of the conclusions' occurrence. In all three studies, participants rated explanations as more probable than refutations. The results imply that individuals create explanations to resolve an inconsistency and that these explanations lead to changes in belief. Changes in belief are therefore of secondary importance to the primary goal of explanation.     

Hidden conflicts: explanations make inconsistencies harder to detect

A rational response to an inconsistent set of propositions is to revise it in a minimal way to restore consistency. A more important psychological goal is usually to create an explanation that resolves the inconsistency. We report five studies showing that once individuals have done so, they find inconsistencies harder to detect. Experiment 1 established the effect when participants explained inconsistencies, and Experiment 2 eliminated the possibility that the effect was a result of demand characteristics. Experiments 3a and 3b replicated the result, and showed that it did not occur in control groups that evaluated (or justified) which events in the pairs of assertions were more surprising. Experiment 4 replicated the previous findings, but the participants carried out all the conditions acting as their own controls. In all five studies, control conditions established that participants were able to detect comparable inconsistencies. Their explanations led them to re-interpret the generalizations as holding by default, and so they were less likely to treat the pairs of assertions as inconsistent. Explanations can accordingly undo the devastating consequences of logical inconsistencies, but at the cost of a subsequent failure to detect them.     

Changing your mind

When individuals detect an inconsistency in a set of propositions, they tend to change their minds about at least one proposition to resolve the inconsistency. The orthodox view from William James (1907) onward has been that a rational change should be minimal. We propose an alternative hypothesis according to which individuals seek to resolve inconsistencies by explaining their origins. We report four experiments corroborating the explanatory hypothesis. Experiment 1 showed that participants’ explanations revised general conditional claims rather than specific categorical propositions. Experiment 2 showed that, when explanations did revise the categorical proposition, participants also tended to deny the consequences of a second generalization. Experiment 3 showed that this tendency persists when participants previously affirmed these consequences explicitly. Experiment 4 showed that, when participants could easily explain an inconsistency by revising a generalization, they were more likely to accept the consequences of a second generalization. All four results contravene minimalism but support the explanatory hypothesis.     

Counterexamples in sentential reasoning

How do logically naive individuals determine that an inference is invalid? In logic, there are two ways to proceed: (1) make an exhaustive search but fail to find a proof of the conclusion and (2) use the interpretation of the relevant sentences to construct a counterexample—that is, a possibility consistent with the premises but inconsistent with the conclusion. We report three experiments in which the strategies that individuals use to refute invalid inferences based on sentential connectives were examined. In Experiment 1, the participants’ task was to justify their evaluations, and it showed that they used counterexamples more often than any other strategy. Experiment 2 showed that they were more likely to use counterexamples to refute invalid conclusions consistent with the premises than to refute invalid conclusions inconsistent with the premises. In Experiment 3, no reliable difference was detected in the results between participants who wrote justifications and participants who did not.     

Changing False Beliefs from Repeated Advertising: The Role of Claim‐Refutation Alignment

This research addresses refutation of false beliefs formed on the basis of repeated exposure to advertisements. Experiment 1 explores belief in the refutation as a function of the perceptual details shared (alignment) between the claim and the refutation as manipulated by whether the original claim was direct (assertion) or indirect (implication). Experiment 2 then examines whether this effect will carry through to belief in the original claim after exposure to the refutation. Findings indicate that direct refutations of indirect claims are believed more than refutations of direct claims. However, direct refutations of direct claims are more effective in reducing belief in the original claim. We argue that recollection of the original claim facilitates automatic updating of belief in that claim. Experiment 3 demonstrates that an alternative cue (a logo) in a refutation that facilitates recall of the original claim enables reduction of belief in the original indirect claim; this finding helps to pin down the mechanism—recall of the original claim—underlying belief updating. Further, Experiment 3 finds that multiple cues to recalling the original claim may prevent the automatic updating process. Theoretical and practical implications are discussed.     

Reasoning from inconsistency to consistency

This article presents a theory of how individuals reason from inconsistency to consistency. The theory is based on 3 main principles. First, individuals try to construct a single mental model of a possibility that satisfies a current set of propositions, and if the task is impossible, they infer that the set is inconsistent. Second, when an inconsistency arises from an incontrovertible fact, they retract any singularly dubious proposition or any proposition that is inconsistent with the fact; otherwise, they retract whichever proposition mismatches the fact. A mismatch can arise from a proposition that has only mental models that conflict with the fact or fail to represent it. Third, individuals use their causal knowledge-in the form of models of possibilities-to create explanations of what led to the inconsistency. A computer program implements the theory, and experimental results support each of its principles.     

Evidence for improved conclusion accuracy after reading about rather than conducting a belief‐inconsistent simple physics experiment

Prior beliefs that contradict data may interfere with the ability to draw accurate conclusions; however, evidence shows that through engaged activity individuals may learn new information. In Experiment 1 , undergraduates performed or read about two physics experiments involving a ball and ramp. The first experiment was consistent with most people's prior beliefs, while the second was inconsistent with most people's prior beliefs. Participants' predictions, experimentation adequacy, conclusions and ability to generalize knowledge were measured to determine the effects of prior belief bias depending on whether participants conducted or read about the experiment. In Experiment 2, a structured hands‐on condition was included and developmental trends across adolescence and adulthood were examined. In both Experiments, reading about a belief‐inconsistent experiment led to improved conclusion accuracy and ability to generalize knowledge as compared to performing the experiment. This was the case when experiments were performed well and after a 12‐week delay for adolescents. Copyright © 2009 John Wiley & Sons, Ltd.     

True overconfidence: The inability of rational information processing to account for apparent overconfidence

The better-than-average effect describes the tendency of people to perceive their skills and virtues as being above average. We derive a new experimental paradigm to distinguish between two possible explanations for the effect, namely rational information processing and overconfidence. Experiment participants evaluate their relative position within the population by stating their complete belief distribution. This approach sidesteps recent methodology concerns associated with previous research. We find that people hold beliefs about their abilities in different domains and tasks which are inconsistent with rational information processing. Both on an aggregated and an individual level, they show considerable overplacement. We conclude that overconfidence is not only apparent overconfidence but rather the consequence of a psychological bias.     

Inconsistencies in extensive games

In certain finite extensive games with perfect information, Cristina Bicchieri (1989) derives a logical contradiction from the assumptions that players are rational and that they have common knowledge of the theory of the game. She argues that this may account for play outside the Nash equilibrium. She also claims that no inconsistency arises if the players have the minimal beliefs necessary to perform backward induction. We here show that another contradiction can be derived even with minimal beliefs, so there is no paradox of common knowledge specifically. These inconsistencies do not make play outside Nash equilibrium plausible, but rather indicate that the epistemic specification must incorporate a system for belief revision. Whether rationality is common knowledge is not the issue.     

Using temporal information to construct, update, and retrieve situation models of narratives

Four experiments explored how readers use temporal information to construct and update situation models and retrieve them from memory. In Experiment 1, readers spontaneously constructed temporal and spatial situation models of single sentences. In Experiment 2, temporal inconsistencies caused problems in updating situation models similar to those observed previously for other dimensions of situation models. In Experiment 3, merely implied temporal order information was inferred from narratives, affecting comprehension of later sentences like explicitly stated order information. Moreover, inconsistent temporal order information prevented the creation and storage in memory of an integrated situation model. In Experiment 4, a temporal inconsistency increased processing time even if readers were unable to report the inconsistency. These results confirm the significance of the temporal dimension of situation models.     

Children's beliefs about instances of mechanical and electrical causation

Two main questions were asked regarding young children's beliefs about causal mediation: What sorts of beliefs about causal mediation are reflected by children's incomplete explanations of causal situations? In particular, do children hold a false belief in action at a distance or do they realize that something must mediate between cause and effect? When presented with a non-visible connection between cause and effect (Experiment I), the children's incomplete (Piagetion Stage 1) explanations either reflected the correct expectation of a mediating connection or else merely reflected identification of the causal agent and no concern one way or another with the issue of causal mediation. This was also the case when the mediating connection was visible and present at the outset (Experiment II). In neither experiment (both of which involved mechanical causation) was there evidence of a false belief in action at a distance. A third experiment involved instances of electrical causation in order to maximize the chances of tapping a false belief. The rationale was that, in their everyday lives, although children do have first-hand experience with the mediating connection in instances of mechanical causation, they do not have such experience with instances of electrical causation. The results from the third experiment were analogous to the results in the other two. It was concluded that, with respect to instances of physical causality, young children do not hold a false belief (in action at a distance) that is later relinquished. Rather, their concerns are, at first, restricted to identifying the causal agent and do not include any beliefs, true or false, about the issue of causal mediation. When they eventually do deal with the question of causal mediation, children hold approximately correct beliefs. In terms of school situations, these findings suggest a shift from providing the child with disconfirming data that will aid him in relinquishing his false beliefs to providing him, instead, with additional data that will supplement his existing, approximately correct beliefs.     

Scientific reasoning in a real‐world context: The effect of prior belief and outcome on children's hypothesis‐testing strategies

The impact of event outcome and prior belief on scientific reasoning was investigated within a real‐world oral health context. Participants (N= 144; ranging from 3 to 11 years) were given hypothesis‐testing tasks and asked to explain their answers. Participants were presented with information that was either consistent or inconsistent with their own beliefs. Each task consisted of scenarios in which the outcome was either good or bad oral health. When the information was belief consistent and the outcome was good, or when the information was belief inconsistent and the outcome was bad, children were more likely to choose scientifically appropriate tests of the stated hypothesis (i.e. manipulate only one variable). Evidence‐based explanations were associated with scientifically appropriate choices in the good‐outcome, belief‐inconsistent scenario and the belief‐consistent, bad‐outcome scenario. Participants' performance on these tasks is explained by considering the plausibility of causal variables. A control of variables strategy was used to test hypotheses in cases in which the evidence was consistent with participants' beliefs and knowledge of causal mechanisms. In contrast, when the evidence was inconsistent with participants' beliefs, children chose to manipulate behaviours likely to lead to a positive health outcome. These findings demonstrate that context and prior knowledge interact to play an important role in children's scientific reasoning.     

Vitalistic thinking in adults

Vitalistic thinking has traditionally been associated with reasoning about biological phenomena. The current research aimed to investigate a broader range of vitalistic thinking than previously studied. Esoteric notions of ‘energy’ are frequently used by individuals when making causal attributions for strange occurrences, and previous literature has linked such thinking with paranormal, magical, and superstitious beliefs. Two experiments are described that aim to investigate whether adults are vitalistic when asked to make causal judgments, and whether this can be predicted by thinking styles and prior paranormal belief. Experiment 1 asked participants to rate three causal options (one of which was vitalistic) for six vignettes. Scores on one dimension of paranormal belief (New Age Philosophy) and analytical thinking significantly predicted vitalism, but scores on intuitive thinking and Traditional Paranormal Beliefs did not. Experiment 2 extended the findings by asking participants to generate their own causal responses. Again, paranormal belief was found to be the best predictor of vitalism, but this time Traditional Paranormal Beliefs were associated with vitalistic responses whilst both intuitive and analytical thinking were unable to significantly predict classification. Results challenge previous findings, suggesting that vitalistic thinking may operate differently when applied to everyday causal reasoning.     

Belief, its inconsistency, and the implications for the teaching faculty

The traditional concept of belief is analyzed and compared with a behavior analytic concept of belief. Beliefs and belief statements are differentiated and relationships between them are examined. The often troublesome inconsistencies in people's beliefs are examined in general and explained, including the phenomena of compartmentalization and repression. Social implications are pursued relative to both punishment for inconsistency in belief and counter-controls thwarting such punishment. The role of teachers in shaping beliefs is analyzed, and appropriate teaching strategies are reviewed.     

Scientific faith: Belief in science increases in the face of stress and existential anxiety

Growing evidence indicates that religious belief helps individuals to cope with stress and anxiety. But is this effect specific to supernatural beliefs, or is it a more general function of belief — including belief in science? We developed a measure of belief in science and conducted two experiments in which we manipulated stress and existential anxiety. In Experiment 1, we assessed rowers about to compete (high-stress condition) and rowers at a training session (low-stress condition). As predicted, rowers in the high-stress group reported greater belief in science. In Experiment 2, participants primed with mortality (vs. participants in a control condition) reported greater belief in science. In both experiments, belief in science was negatively correlated with religiosity. Thus, some secular individuals may use science as a form of “faith” that helps them to deal with stressful and anxiety-provoking situations.     

Background beliefs and evidence interpretation

In this paper we argue that it is often adaptive to use one's background beliefs when interpreting information that, from a normative point of view, is incomplete. In both of the experiments reported here participants were presented with an item possessing two features and were asked to judge, in the light of some evidence concerning the features, to which of two categories it was more likely that the item belonged. It was found that when participants received evidence relevant to just one of these hypothesised categories (i.e. evidence that did not form a Bayesian likelihood ratio) they used their background beliefs to interpret this information. In Experiment 2, on the other hand, participants behaved in a broadly Bayesian manner when the evidence they received constituted a completed likelihood ratio. We discuss the circumstances under which participants, when making their judgements, consider the alternative hypothesis. We conclude with a discussion of the implications of our results for an understanding of hypothesis testing, belief revision, and categorisation.     

Grounded spatial belief revision

Beliefs frequently undergo revisions, especially when new pieces of information are true but inconsistent with current beliefs. In previous studies, we showed that linguistic asymmetries provided by relational statements, play a crucial role in spatial belief revision. Located objects (LO) are preferably revised compared to reference objects (RO), known as the LO-principle. Here we establish a connection between spatial belief revision and grounded cognition. In three experiments, we explored whether imagined physical object properties influence which object is relocated and which remains at its initial position. Participants mentally revised beliefs about the arrangements of objects which could be envisaged as light and heavy (Experiment 1), small and large (Experiment 2), or movable and immovable (Experiment 3). The results show that intrinsic object properties are differently taken into account during spatial belief revision. Object weight did not alter the LO-principle (Experiment 1), whereas object size was found to influence which object was preferably relocated (Experiment 2). Object movability did not affect relocation preferences but had an effect on relocation durations (Experiment 3). The findings support the simulation hypothesis within the grounded cognition approach and create new connections between the spatial mental model theory of reasoning and the idea of grounded cognition.     

Naïve predictions of motion and orientation in mirrors: From what we see to what we expect reflections to do

The study aimed to investigate naïve beliefs regarding the dynamic and static behavior of reflections. In the first three experiments, participants in the study made predictions about the correspondence between real and reflected movements or about the orientation of the reflection of a static object placed in front of a mirror. In Experiments 1 and 2, paper-and-pencil tasks were used and in Experiment 3 participants were asked to make their predictions while imagining that they were facing a mirror. Results revealed that a percentage of undergraduates (ranging from 25% to 35%) were unable to make correct predictions. We classified the errors into types and found that responses either conform to the belief that reflections do the same or that they do the opposite. This suggests an oversimplification of the geometry of mirror reflections in two directions: participants either generalize what they see when movements are parallel to the mirror or what they see when movements are orthogonal to the mirror. Findings from Experiment 4 confirmed that these two expectations fit in with what people perceive in mirrors. Findings from Experiment 5 confirmed that this is also in agreement with the relationship perceived when looking at similar movements and orientations “outside” mirrors.     

Perceiving emotions: Cueing social categorization processes and attentional control through facial expressions

Individuals spontaneously categorise other people on the basis of their gender, ethnicity and age. But what about the emotions they express? In two studies we tested the hypothesis that facial expressions are similar to other social categories in that they can function as contextual cues to control attention. In Experiment 1 we associated expressions of anger and happiness with specific proportions of congruent/incongruent flanker trials. We also created consistent and inconsistent category members within each of these two general contexts. The results demonstrated that participants exhibited a larger congruency effect when presented with faces in the emotional group associated with a high proportion of congruent trials. Notably, this effect transferred to inconsistent members of the group. In Experiment 2 we replicated the effects with faces depicting true and false smiles. Together these findings provide consistent evidence that individuals spontaneously utilise emotions to categorise others and that such categories determine the allocation of attentional control.