Response demands and the recruitment of heuristic strategies in syllogistic reasoning

Abstract

Two experiments investigated whether dealing with a homogeneous subset of syllogisms with time-constrained responses encouraged participants to develop and use heuristics for abstract (Experiment 1) and thematic (Experiment 2) syllogisms. An atmosphere-based heuristic accounted for most responses with both abstract and thematic syllogisms. With thematic syllogisms, a weaker effect of a belief heuristic was also observed, mainly where the correct response was inconsistent with the atmosphere of the premises. Analytic processes appear to have played little role in the time-constrained condition, whereas their involvement increased in a self-paced, unconstrained condition. From a dual-process perspective, the results further specify how task demands affect the recruitment of heuristic and analytic systems of reasoning. Because the syllogisms and experimental procedure were the same as those used in a previous neuroimaging study by Goel, Buchel, Frith, and Dolan (2000), the result also deepen our understanding of the cognitive processes investigated by that study.

Keywords:

• Reasoning
• Deduction
• Syllogisms
• Heuristics
• Atmosphere effect
• Belief bias
• Mental models
• Neuroimaging

We thank Tom Ormerod and two anonymous referees for their helpful comments. For the same reason, and for having provided the original materials, we thank Vinod Goel.

Notes

¹ The 15 syllogisms used in the 2003 study by Goel and Dolan differed from those used in 2000 by Goel et al. for four items. However, even for those syllogisms the correct solution coincides with the solution suggested by an atmosphere-based heuristic strategy. Of the 24 syllogisms used in the 2004 study, 15 had a valid conclusion consistent with atmosphere, 1 had a valid conclusion not consistent with atmosphere (ae1), and the rest were invalid. Whether invalid syllogisms are consistent or not with atmosphere depends on the specific conclusion proposed to the participants. This information is not available in the paper. Both in the 2003 and in the 2004 studies the time constraint remained as in the 2000 study.

² The five couple of premises with no conclusions consistent with the atmosphere are:

1. No A are B, all B are C (conclusion: Some C are not A).

2. No B are A, all B are C (conclusion: Some C are not A).

3. All B are A, no B are C (conclusion: Some A are not C).

4. All B are A, no C are B (conclusion: Some A are not C).

5. All B are A, all B are C (conclusion: Some A are C).

In this paper, like in most psychological studies on syllogistic reasoning and in many logical systems, we assume that the universally quantified premises have an existential entailment. In the logical systems where this assumption is rejected none of the syllogisms above entails any valid conclusion— for example, “all B are A, all B are C” does not entail “some A are C”, because the latter is not necessarily true when the B set is empty.

³ We used 46 arguments, instead of 30 as in Goel et al. (2000), in order to have more data points to observe whether some learning occurred during the task (see the Results section).

⁴“Training set” is an appropriate name from the perspective of the experimenters. However, the training and test sets did not differ in any way from the perspective of the participants: There were no interruptions between the two sets, the stimuli presentation and response constraints were the same, there were no feedbacks, and so on. That is, the training set in the constrained condition should not be confounded with the explicit, preexperimental training with accuracy feedback administered to participants in the unconstrained condition.

⁵ This design imbalance is due to a structural feature of categorical syllogisms themselves, rather than to a bias in our selection of the stimuli.

⁶ We believe that Items 1 and 8 were not sufficiently diagnostic, and we did not use them. Instead of formulating Item 4 as a yes/no question, we required answering on a Likert scale. In our version, “5” corresponded to “a lot”.