From falsification to generating an alternative hypothesis: Exploring the role of the new-perspective hypothesis in successful 2-4-6 task performance
Journal
Thinking and Reasoning
Journal Volume
17
Journal Issue
2
Pages
105-136
Date Issued
2011
Author(s)
Lien, Y.-W.
Abstract
Abstract Previous research has found no consistent relationship between measures of disconfirmatory evidence, alternative hypotheses, and people's success in rule-discovery tasks. The present paper explores falsification's inductive benefit under the “context of discovery” in Wason's 2‐4‐6 task by developing a new type of alternative hypothesis, which we label the “new-perspective hypothesis”. Experiment 1 found that falsification is effective only when a new-perspective hypothesis is generated, rather than a same-perspective hypothesis. The total number of alternative hypotheses was also unrelated to rule-discovery success. Experiment 2 replicated Experiment 1 but included the addition of a different name-content task as well as two levels of task difficulty. The main findings were similar to those for Experiment 1, and the new-perspective hypothesis was observed to be most important for the difficult rule-discovery task. These results help to clarify the important ways new-perspective hypotheses and disconfirmatory evidence contribute to successful rule-discovery performance. Keywords: Disconfirmatory evidenceAlternative hypothesisNew-perspective hypothesisWason's taskRule-discovery Acknowledgments This research was supported by a grant to Yunn-Wen Lien from National Science Council of Taiwan (NSC 89-2413-H-002-040). We thank Professor Jonathan St. B.T. Evans, Dr Fenna Poletiek, and other anonymous reviewers for their extremely helpful comments on the draft. We thank Yu-Shen Lin for conducting the 2nd experiment. We are especially grateful to Arthur and Byerly Woodward for their suggestions on the manuscript and proofreading. Notes 1Poletiek (Citation2001, Citation2004) derived a behavioural index, the severity of a test, from Popper's falsification philosophy, which is equated with the number of alternative hypotheses that one test excludes. This index was significantly correlated to the amount of falsification (the third definition mentioned in our study) a participant could get. We did not include this measure in the present study. 2Some types of hypotheses (e.g., “a + b = c” or “a + b + c = 12”) were excluded, since they were mentioned by less than 5% of the participants. 3As for the examples illustrating the concepts of same- and new-perspective hypotheses here, revising “evens” to “integers” (a same-perspective hypothesis) is a broadening of the initial hypothesis, while revising “evens” to “evens different by 2” (a new-perspective hypothesis) is a restriction of the original one. However, a same-perspective hypothesis does not necessarily represent a broadening, and a new-perspective hypothesis does not necessarily represent a restriction. For example, when the hypothesis “numbers between 1 and 10” is revised to “numbers between 1 and 100”, this hypothesis is categorised as both a same-perspective hypothesis and a broadening hypothesis. Similarly, when a reasoner revises the hypothesis “evens” to “ascending numbers”, this is not a restriction of the original hypothesis but is categorised as a new-perspective hypothesis. These cases have been empirically observed in our participants. Setting different relationships between initial hypotheses and target rules (embedded, overlapping, and surrounding), Klayman and Ha (Citation1989) also found that the relation between hypotheses was continually subject to change. The key point of distinguishing between same- or new-perspective hypotheses is to demonstrate participants' breadth of searching within the hypothesis space. 4Following the discriminant analysis, a Bayesian rule with equal prior probabilities was used to calculate the percentage of correct classification of the successful and unsuccessful performers in which the actual results were compared with predicted results derived from a linear combination of goal variables in a regression analysis. 5The first character of the first name means “yellow”, the third character of the second name means “red”, and the first character of the third name means “blue”. 6We hypothesise two reasons why this analysis did not reach the significant level: (1) The number of successful participants in both conditions was small, and (2) the difference in the hypothesis spaces is not very large. The authors have compared the speed of successfully finding the rules in the number-content task and another version of the 2‐4‐6 problem—the poker content, which used three poker cards as initial instances in another study (Chen, Citation2008). With 11 main branches in the basic hypothesis structure of the poker content, we found that successful participants in the poker content condition discovered the correct rule significantly slower than successful participants in the number condition.
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Type
journal article