Considering too few alternatives: The mental model theory of extensional reasoning

When solving a simple probabilistic problem, people tend to build an incomplete mental representation. We observe this pattern in responses to probabilistic problems over a set of premises using the conjunction, disjunction, and conditional propositional connectives. The mental model theory of extensional reasoning explains this bias towards underestimating the number of possibilities: In reckoning with different interpretations of the premises (logical rules, mental model theoretical, and, specific to conditional premises, conjunction and biconditional interpretation) the mental model theory accounts for the majority of observations. Different interpretations of a premise result in a build-up of mental models that are often incomplete. These mental models are processed using either an extensional strategy relying on proportions amongst models, or a conflict monitoring strategy. The consequence of considering too few possibilities is an erroneous probability estimate akin to that faced by decision makers who fail to generate and consider all alternatives, a characteristic of bounded rationality. We compare our results to the results published by Johnson-Laird, Legrenzi, Girotto, Legrenzi, and Caverni [Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar], 62 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]–88 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]. doi:10 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar].1037 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]/0033 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]-295X Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar].106 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar].1 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar].62 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]], and we observe lower performance levels than those in the original article.     

When will is not the same as should: The role of modals in reasoning with legal conditionals

Naïve reasoners reject logically valid conclusions from conditional rules if they can think of exceptions in which the antecedent is true, but the consequent is not. However, when reasoning with legal conditionals (e.g., “If a person kills another human, then this person should be punished for manslaughter”) people hardly consider exceptions but evaluate conclusions depending on their own sense of justice. We show that participants’ reluctance to consider exceptions in legal reasoning depends on the modal auxiliary used. In two experiments we phrased legal conditionals either with the modal “should” (i.e., “ . . . then this person should be punished”), or with “will” (i.e., “ . . . then this person will be punished”) and presented them as modus ponens or modus tollens inferences. Participants had to decide whether the offender should or will be punished (modus ponens) or whether the offender indeed committed the offence (modus tollens). For modus ponens inferences phrased with “should” we replicate previous findings showing that participants select conclusions on the basis of their own sense of justice (Experiments 1 and 2). Yet, when the legal conditional is phrased with the modal “will” this effect is attenuated (Experiments 1 and 2), and exceptions are considered (Experiment 1). The modal auxiliary did not affect modus tollens inferences.     

Moral foundations and political attitudes: The moderating role of political sophistication

Political attitudes can be associated with moral concerns. This research investigated whether people's level of political sophistication moderates this association. Based on the Moral Foundations Theory, this article examined whether political sophistication moderates the extent to which reliance on moral foundations, as categories of moral concerns, predicts judgements about policy positions. With this aim, two studies examined four policy positions shown by previous research to be best predicted by the endorsement of Sanctity, that is, the category of moral concerns focused on the preservation of physical and spiritual purity. The results showed that reliance on Sanctity predicted political sophisticates' judgements, as opposed to those of unsophisticates, on policy positions dealing with equal rights for same‐sex and unmarried couples and with euthanasia. Political sophistication also interacted with Fairness endorsement, which includes moral concerns for equal treatment of everybody and reciprocity, in predicting judgements about equal rights for unmarried couples, and interacted with reliance on Authority, which includes moral concerns for obedience and respect for traditional authorities, in predicting opposition to stem cell research. Those findings suggest that, at least for these particular issues, endorsement of moral foundations can be associated with political attitudes more strongly among sophisticates than unsophisticates.     

Implicit sequence learning in ring‐tailed lemurs (Lemur catta)

Implicit learning involves picking up information from the environment without explicit instruction or conscious awareness of the learning process. In nonhuman animals, conscious awareness is impossible to assess, so we define implicit learning as occurring when animals acquire information beyond what is required for successful task performance. While implicit learning has been documented in some nonhuman species, it has not been explored in prosimian primates. Here we ask whether ring‐tailed lemurs (Lemur catta) learn sequential information implicitly. We tested lemurs in a modified version of the serial reaction time task on a touch screen computer. Lemurs were required to respond to any picture within a 2 × 2 grid of pictures immediately after its surrounding border flickered. Over 20 training sessions, both the locations and the identities of the images remained constant and response times gradually decreased. Subsequently, the locations and/or the identities of the images were disrupted. Response times indicated that the lemurs had learned the physical location sequence required in original training but did not learn the identity of the images. Our results reveal that ring‐tailed lemurs can implicitly learn spatial sequences, and raise questions about which scenarios and evolutionary pressures give rise to perceptual versus motor‐implicit sequence learning.     

On Using Ethical Theories to Teach Engineering Ethics

Many engineering ethics classes and textbooks introduce theories such as utilitarianism and Kantianism (and most others draw from these theories without mentioning them explicitly). Yet using ethical theories to teach engineering ethics is not devoid of difficulty. First, their status is unclear (should one pick a single theory or use them all? does it make a difference?) Also, textbooks generally assume or fallaciously ‘prove’ that egoism (or even simply accounting for one’s interests) is wrong. Further, the drawbacks of ethical theories are underestimated and the theories are also otherwise misrepresented to make them more suitable for engineering ethics as the authors construe it, viz. the ‘moral reasoning’ process. Stating in what various theories disagree would allow the students to frame the problem more productively in terms of motive–consequence or society–individual dichotomies rather than in terms of Kant–utilitarian.     

Optimal Predictions in Everyday Cognition: The Wisdom of Individuals or Crowds?

Griffiths and Tenenbaum (2006) asked individuals to make predictions about the duration or extent of everyday events (e.g., cake baking times), and reported that predictions were optimal, employing Bayesian inference based on veridical prior distributions. Although the predictions conformed strikingly to statistics of the world, they reflect averages over many individuals. On the conjecture that the accuracy of the group response is chiefly a consequence of aggregating across individuals, we constructed simple, heuristic approximations to the Bayesian model premised on the hypothesis that individuals have access merely to a sample of k instances drawn from the relevant distribution. The accuracy of the group response reported by Griffiths and Tenenbaum could be accounted for by supposing that individuals each utilize only two instances. Moreover, the variability of the group data is more consistent with this small-sample hypothesis than with the hypothesis that people utilize veridical or nearly veridical representations of the underlying prior distributions. Our analyses lead to a qualitatively different view of how individuals reason from past experience than the view espoused by Griffiths and Tenenbaum.     

幼儿反事实推理的错误源分析

本研究选取57名3~5岁幼儿,考察了在两种选择和三种选择的反事实推理任务中儿童的表现以及是否出现现实错误。结果如下:无论在两种还是三种选择的反事实任务中,3岁组儿童的得分显著低于4岁和5岁组儿童,而4岁和5岁组儿童之间不存在显著差异;幼儿在反事实推理中的确会出现现实错误,但除此之外,幼儿在三种选择任务中也会选择现实和正确答案之外的第三个选项。由此可见,年幼儿童可能在抑制现实和建构反事实替代情境方面都存在困难,这尚需我们进一步探究。     

大学生的认知风格与逻辑推理的关系

以大学生为被试,探讨认知风格与逻辑推理的关系。结果表明：（1）在三段论推理中,场依存型学生和场独立型学生推理成绩不存在显著差异,学过和未学过逻辑学的学生推理成绩也不存在显著差异,但男生和女生推理成绩差异显著,女生比男生更易受“气氛”的影响。（2）在命题推理中,对抽象材料构成的命题,场独立型学生和场依存型学生的推理存在显著差异,场独立型学生表现出更强的证伪倾向,场依存型学生表现出更强的换位倾向;对具体材料构成的命题,场独立型学生和场依存型学生的推理不存在显著差异。     

THOG问题促进效应研究

通过选取经典的THOG问题作为实验材料,探讨了大学生解决具体以及抽象选言推理问题的认知机制,结果发现:(1)具体内容的选言推理问题对抽象内容的选言推理问题有明显的促进效应,表现为先解决逃犯问题后解决THOG问题组的正确率显著高于先解决THOG问题后解决逃犯问题组;(2)提供笼统的解题策略对大学生解决THOG问题几乎没有促进作用。     

Linda问题:"齐当别"抉择模型的解释

大量有关人类归因判断的研究表明,人类经常违反理性概率公理.Tversky和Kahneman(1983)使用Linda问题等特定场景的研究发现,人们系统性地表现出违反理性推断标准,判断合取事件发生概率大于其组成事件发生概率,称之为合取谬误,并用人们使用代表性启发式判断概率来解释该现象产生的原因.然而使用启发式观点对合取谬误现象进行解释过于模糊不清.该文首先介绍了合取谬误现象及其解释模型,然后应用Li(1994,2004)提出的不确定情形下决策理论--"齐当别"抉择模型对Linda问题中合取谬误产生的原因进行了新的解释.