Priming divergent thinking promotes logical reasoning in 6- to 8-year olds: But more for high than low SES students

Divergent thinking is a component of creativity. In the following study, we argue that this form of thinking also underlies logical reasoning. A total of 205 early elementary school children in Grades 1 and 2, from high and moderately low SES environments, were given a short-term prime for divergent thinking and simple reasoning problems. Overall, receiving this prime significantly improved logical reasoning at both grade levels. High and low SES students had similar levels of working memory, inhibitory control, performance on the divergent thinking task, and levels of logical reasoning without the prime. However, also consistent with our predictions, only high SES students showed overall improved logical reasoning following the divergent thinking prime, with the SES difference concentrated in the younger students. These results suggest that environmental differences in openness to alternatives and divergent thinking might underlie developing SES differences in levels of logical thinking.     

Intuition and The Junctures of Judgment in Decision Procedures for Clinical Ethics

Moral decision procedures such as principlism or casuistry require intuition at certain junctures, as when a principle seems indeterminate, or principles conflict, or we wonder which paradigm case is most relevantly similar to the instant case. However, intuitions are widely thought to lack epistemic justification, and many ethicists urge that such decision procedures dispense with intuition in favor of forms of reasoning that provide discursive justification. I argue that discursive justification does not eliminate or minimize the need for intuition, or constrain our intuitions. However, this is not a problem, for intuitions can be justified in easy or obvious cases, and decision procedures should be understood as heuristic devices for reaching judgments about harder cases that approximate the justified intuitions we would have about cases under ideal conditions, where hard cases become easy. Similarly, the forms of reasoning which provide discursive justification help decision procedures perform this heuristic function not by avoiding intuition, but by making such heuristics more accurate. Nonetheless, it is possible to demand too much justification; many clinical ethicists lack the time and philosophical training to reach the more elaborate levels of discursive justification. We should keep moral decision procedures simple and user-friendly so that they will provide what justification can be achieved under clinical conditions, rather than trying to maximize our epistemic justification out of an overstated concern about intuition.     

Not so fast! (and not so frugal!): rethinking the recognition heuristic

The 'fast and frugal' approach to reasoning (Gigerenzer, G., & Todd, P. M. (1999). Simple heuristics that make us smart. New York: Oxford University Press) claims that individuals use non-compensatory strategies in judgment--the idea that only one cue is taken into account in reasoning. The simplest and most important of these heuristics postulates that judgment sometimes relies solely on recognition. However, the studies that have investigated usage of the recognition heuristic have confounded recognition with other cues that could also lead to similar judgments. This paper tests whether mere recognition is actually driving the findings in support of the recognition heuristic. Two studies provide evidence that judgments do not conform to the recognition heuristic when these confounds are accounted for. Implications for the study of simple heuristics are discussed.     

How (far) can rationality be naturalized?

The paper shows why and how an empirical study of fast-and-frugal heuristics can provide norms of good reasoning, and thus how (and how far) rationality can be naturalized. We explain the heuristics that humans often rely on in solving problems, for example, choosing investment strategies or apartments, placing bets in sports, or making library searches. We then show that heuristics can lead to judgments that are as accurate as or even more accurate than strategies that use more information and computation, including optimization methods. A standard way to defend the use of heuristics is by reference to accuracy-effort trade-offs. We take a different route, emphasizing ecological rationality (the relationship between cognitive heuristics and environment), and argue that in uncertain environments, more information and computation are not always better (the ??less-can-be-more?? doctrine). The resulting naturalism about rationality is thus normative because it not only describes what heuristics people use, but also in which specific environments one should rely on a heuristic in order to make better inferences. While we desist from claiming that the scope of ecological rationality is unlimited, we think it is of wide practical use.     

We favor formal models of heuristics rather than lists of loose dichotomies: a reply to Evans and Over

In their comment on Marewski et al. (good judgments do not require complex cognition, 2009) Evans and Over (heuristic thinking and human intelligence: a commentary on Marewski, Gaissmaier and Gigerenzer, 2009) conjectured that heuristics can often lead to biases and are not error free. This is a most surprising critique. The computational models of heuristics we have tested allow for quantitative predictions of how many errors a given heuristic will make, and we and others have measured the amount of error by analysis, computer simulation, and experiment. This is clear progress over simply giving heuristics labels, such as availability, that do not allow for quantitative comparisons of errors. Evans and Over argue that the reason people rely on heuristics is the accuracy-effort trade-off. However, the comparison between heuristics and more effortful strategies, such as multiple regression, has shown that there are many situations in which a heuristic is more accurate with less effort. Finally, we do not see how the fast and frugal heuristics program could benefit from a dual-process framework unless the dual-process framework is made more precise. Instead, the dual-process framework could benefit if its two “black boxes” (Type 1 and Type 2 processes) were substituted by computational models of both heuristics and other processes.     

The probability heuristics model of syllogistic reasoning

A probability heuristic model (PHM) for syllogistic reasoning is proposed. An informational ordering over quantified statements suggests simple probability based heuristics for syllogistic reasoning. The most important is the "min-heuristic": choose the type of the least informative premise as the type of the conclusion. The rationality of this heuristic is confirmed by an analysis of the probabilistic validity of syllogistic reasoning which treats logical inference as a limiting case of probabilistic inference. A meta-analysis of past experiments reveals close fits with PHM. PHM also compares favorably with alternative accounts, including mental logics, mental models, and deduction as verbal reasoning. Crucially, PHM extends naturally to generalized quantifiers, such as Most and Few, which have not been characterized logically and are, consequently, beyond the scope of current mental logic and mental model theories. Two experiments confirm the novel predictions of PHM when generalized quantifiers are used in syllogistic arguments. PHM suggests that syllogistic reasoning performance may be determined by simple but rational informational strategies justified by probability theory rather than by logic.     

逻辑－信念冲突与推理难度对逻辑和信念判断的影响

双加工理论框架下的平行竞争模型和默认干涉模型对推理过程中启发式和分析式加工的启动次序和相互作用的性质提出了不同假设。本研究通过考察被试在信念判断和逻辑判断两种指导语下解决不同难度和不同类型推理问题的正确率和反应时,对两个模型的预测进行了检验。实验结果表明,解决简单问题时,问题类型对信念判断有显著影响,对逻辑判断无显著影响;解决复杂问题时,问题类型对逻辑判断的影响显著大于对信念判断的影响。实验结果支持平行竞争模型的假设,即两类加工在推理过程中同时启动,共同竞争最终的推理反应。     

When the brain decides: a familiarity-based approach to the recognition heuristic as evidenced by event-related brain potentials

Humans can make fast and highly efficient decisions by using simple heuristics that are assumed to exploit basic cognitive functions. In the study reported here, we used event-related potentials (ERPs) to disclose the psychological mechanisms underlying one of the most frugal decision rules, namely, the recognition heuristic. According to this heuristic, whenever two objects have to be ranked by a specific criterion and only one object is recognized, the recognized object is ranked higher than the unrecognized object. Using a standard recognition-heuristic paradigm, we predicted participants' decisions by analyzing an ERP correlate of familiarity-based recognition occurring 300 to 450 ms after stimulus onset. The measure remained a significant predictor even when later ERP correlates were taken into account. These findings are evidence for the thesis that simple heuristics exploit basic cognitive processes. Specifically, the findings show that familiarity--that is, recognition in the absence of recollection--contributes to decisions made on the basis of such heuristics.     

Against logical generalism

The orthodox view of logic takes for granted the central importance of logical principles. Logic, and thus logical reasoning, is to be understood as a system of rules or principles with universal application. Let us call this orthodox view logical generalism. In this paper we argue that logical generalism, whether monist or pluralist, is wrong. We then outline an account of logical consequence in the absence of general logical principles, which we call logical particularism.

     

Using dual-process theory and analogical transfer to explain facilitation on a hypothetico-deductive reasoning task

Using the analogical transfer paradigm, the present study investigated the competing explanations of Girotto and Legrenzi (Psychological Research 51: 129–135, 1993) and Griggs, Platt, Newstead, and Jackson (Thinking and Reasoning 4: 1–14, 1998) for facilitation on the SARS version of the THOG problem, a hypothetico-deductive reasoning task. Girotto and Legrenzi argue that facilitation is based on logical analysis of the task [System 2 reasoning in Evans’s (Trends in Cognitive Sciences 7: 454–459, 2003) dual-process account of reasoning] while Griggs et al. maintain that facilitation is due to an attentional heuristic produced by the wording of the problem (System 1 reasoning). If Girotto and Legrenzi are correct, then System 2 reasoning, which is volitional and responsible for deductive reasoning, should be elicited, and participants should comprehend the solution principle of the THOG task and exhibit analogical transfer. However, if Griggs et al. are correct, then System 1 reasoning, which is responsible for heuristic problem solving strategies such as an attentional heuristic, should occur, and participants should not abstract the solution principle and transfer should not occur. Significant facilitation (68 and 82% correct) was only observed for the two SARS source problems, but significant analogical transfer did not occur. This lack of transfer suggests that System 1 reasoning was responsible for the facilitation observed in the SARS problem, supporting Griggs et al.’s attentional heuristic explanation. The present results also underscore the explanatory value of using analogical transfer rather than facilitation as the criterion for problem understanding.     

Should reason be fragmented?

Cognitive relativists‐pragmatists (Stich, Churchland) claim that human cognitive strategies, lacking a common goal, are in addition divergent to the point of incommensurability. They appeal to the study of reasoning heuristics for evidence on cognitive diversity and incorrigibility. It is here argued that no such evidence is offered by the research, which, on the contrary (1) presents heuristics as uniform across great variations; (2) offers advice for correcting and improving human reasoning; and (3) very often postulates a uniformity of core logical strategies, built into reasoning competence. Cognitive research thus supports a moderate rationalism rather than relativism‐pragmatism.     

Ignorance or integration: the cognitive processes underlying choice behavior

The fast‐and‐frugal heuristic framework assumes noncompensatory tools for human preferences (i.e., priority heuristic) and inferences (i.e., take the best heuristic). According to this framework, these heuristics predict choice behavior as well as model the cognitive processes underlying such behavior. The current paper presents two studies that juxtapose predictions derived from these two simple heuristics with alternative predictions derived from compensatory principles. Dependent measures that included reaction time, choice pattern, confidence level, and accuracy were better predicted by compensatory indices than by noncompensatory indices. These findings suggest that people do not rely on limited arguments only, but tend to integrate all acquired information into their choice processes. This tendency was replicated even when the experimental task facilitated the use of noncompensatory principles. We argue that the fast and frugal heuristics can predict the final outcome only under certain conditions, but even in these particular situations they are not applicable to the processes underlying choice behavior. An integrative model for choice behavior is proposed that better represents the data. Copyright © 2009 John Wiley & Sons, Ltd.     

Fast and frugal heuristics: rationality and the limits of naturalism

Gerd Gigerenzer and Thomas Sturm have recently proposed a modest form of what they describe as a normative, ecological and limited naturalism. The basic move in their argument is to infer that certain heuristics we tend to use should be used in the right ecological setting. To address this argument, we first consider the case of a concrete heuristic called Take the Best (TTB). There are at least two variants of the heuristic which we study by making explicit the choice functions they induce, extending these variants of TTB beyond binary choice. We argue that the naturalistic argument can be applied to only one of the two variants of the heuristic; we also argue that the argument for the extension requires paying attention to other “rational” virtues of heuristics aside from efficacy, speed, and frugality. This notwithstanding, we show that there is a way of extending the right variant of TTB to obtain a very well behaved heuristic that could be used to offer a stronger case for the naturalistic argument (in the sense that if this heuristic is used, it is also a heuristic that we should use). The second part of the article considers attempts to extending the naturalistic argument from algorithms dealing with inference to heuristics dealing with choice. Our focus is the so-called Priority Heuristic, which we extend from risk to uncertainty. In this setting, the naturalist argument seems more difficult to formulate, if it remains feasible at all. Normativity seems in this case extrinsic to the heuristic, whose main virtue seems to be its ability to describe actual patterns of choice. But it seems that a new version of the naturalistic argument used with partial success in the case of inference is unavailable to solve the normative problem of whether we should exhibit the patterns of choice that we actually display.     

Children’s causal reasoning: Counterfactual thinking occurs for ‘negative’ outcomes only

Harris, German and Mills (Children’s use of counterfactual thinking in causal reasoning. Cognition, 61 (1996), 223–259), following Mackie, argue that children make explicit use of counterfactual thinking in arriving at causal judgments. They showed that children as young as 3, in explaining simple mishap events, made reference to courses of action that a protagonist had rejected, when that course of action would have prevented the observed outcome. It is hypothesized here that such counterfactual thinking might have been invoked by the ‘negative’ mishaps rather than as part of the causal reasoning process. Although the generation of counterfactuals in explanation was replicated using mishap outcomes such as those used by Harris et al., counterfactual thinking was not evident in children’s explanations of ‘positive’ outcomes. These results undermine the view that a counterfactual thinking process, as indexed by reference to possible actions rejected by a protagonist, is necessary for causal reasoning. Alternative characterizations of the relationship between causals and counterfactuals are discussed.     

Reconsidering "evidence" for fast-and-frugal heuristics

In several recent reviews, authors have argued for the pervasive use of fast-and-frugal heuristics in human judgment. They have provided an overview of heuristics and have reiterated findings corroborating that such heuristics can be very valid strategies leading to high accuracy. They also have reviewed previous work that implies that simple heuristics are actually used by decision makers. Unfortunately, concerning the latter point, these reviews appear to be somewhat incomplete. More important, previous conclusions have been derived from investigations that bear some noteworthy methodological limitations. I demonstrate these by proposing a new heuristic and provide some novel critical findings. Also, I review some of the relevant literature often not—or only partially—considered. Overall, although some fast-and-frugal heuristics indeed seem to predict behavior at times, there is little to no evidence for others. More generally, the empirical evidence available does not warrant the conclusion that heuristics are pervasively used.     

Infinite Reasoning

Our relationship to the infinite is controversial. But it is widely agreed that our powers of reasoning are finite. I disagree with this consensus; I think that we can, and perhaps do, engage in infinite reasoning. Many think it is just obvious that we can't reason infinitely. This is mistaken. Infinite reasoning does not require constructing infinitely long proofs, nor would it gift us with non-recursive mental powers. To reason infinitely we only need an ability to perform infinite inferences. I argue that we have this ability. My argument looks to our best current theories of inference and considers examples of apparent infinite reasoning. My position is controversial, but if I'm right, our theories of truth, mathematics, and beyond could be transformed. And even if I'm wrong, a more careful consideration of infinite reasoning can only deepen our understanding of thinking and reasoning.     

Tremor Frequencies

In an attempt to improve logical reasoning performances, 64 introductory psychology students were randomly assigned to experimental and control groups. The experimental condition involved solving logic syllogisms when the obvious “logical error” was not included as a possible answer. Control subjects solved the same problems with the “logical error” included as a choice. An analysis of variance procedure applied to the subjects' logic pretest-posttest gain scores indicated that the experimental group did significantly better than the control group on invalid principles. The results were discussed in terms of Piaget's theory of logical thinking and the possibility of performance rather than competence problems in adult reasoning. The need to develop more effective instructional techniques to enhance transfer of learning was underscored.     

Simple mechanisms for gathering social information

Social contexts are notoriously complex, yet decisions are nevertheless made by using simple strategies. We argue that the concept of fast and frugal heuristics provides a promising framework for understanding how we gather social information to make decisions in social environments. That is, we assume that under limitations of time, energy, and computational resources people use cognitively based shortcuts that rely on information from social environments to solve different types of real problems. We review three successful applications of heuristics to the social arena. We first introduce some commonly faced social inference problems (e.g., selecting a mate or deciding whether to cooperate with someone) and then discuss how individuals can use simple strategies to solve such problems. For each problem, we consider how social environments are structured, and how we take advantage of this structure when using heuristics to make inferences and decisions.     

Human reasoning: Some possible effects of availability

This paper discusses some possible ways in which the availability heuristic (Tversky and Kahneman, 1973) may mediate subjects' responses to experimental ‘reasoning’ tasks. A brief review of some effects of availability in other areas is given and then the application of availability to reasoning data is considered with respect to problems employing both ‘thematic’ and ‘abstract’ content.In the case of thematic content, it is argued, with reference to a variety of studies, that to produce a differential effect (to abstract content), the content must provide available cues, resulting from the subjects' experience. Differential effects of content are thus interpreted as differential effects of availability. When abstract content is used, there are cues available from the experimental situation itself, and it is shown that several known error tendencies readily lend themselves to an explanation in terms of availability.In the final section, it is pointed out that a focus on available cues, rather than logical structure, provides a psychological, rather than logical, approach to human reasoning. It is argued that a bias may be psychologically, although not logically, optimal in that it may often produce correct responses in ‘real life’. Accordingly, the possible real life utility of availability is considered, and several ways in which the bias may lead to usually correct decisions are discussed. Given this, it is argued that availability is an effective heuristic and that observed biases on a range of experimental tasks may thus be interpreted as resulting from the application of a behavior that is optimal within the limits of human cognition. However, it is concluded that limitations in both deterministic and probabilistic problem solving may lead to a consistent, but erroneous, view of the world.