We explored the “context of discovery” in Wason's 2–4–6 task, focusing on how the first hypothesis is generated. According to Oaksford and Chater (1994a) people generate hypotheses extracting “common features”, or regularities, from the available triples, but their model does not explain why some regularities contribute to the hypothesis more than do other regularities. Our conjecture is that some regularities contribute to the hypothesis more than do other regularities because people estimate the amount of information in the perceived regularities and try to preserve as much information as possible in their initial hypotheses. Experiment 1, which used two initial triples, showed that the presence of high-information relational regularities in the initial triples affected the information in the initial hypotheses more than did the presence of low-information object regularities. Experiment 2 extended the results to the classic situation in which only one initial triple is given. It also suggested that amount of information is the only aspect of the structure of the triple that affects hypotheses generation. Experiment 3 confirmed the latter finding: Although relations are commonly distinguished between first-order and higher order relations, the latter being most important for generating hypotheses (Gentner, 1983), higher order relations do have an effect on Wason's 2–4–6 task only if their presence increases information. In the conclusion we discuss the statistical soundness of human hypotheses generation processes, and we ask an unanswered question: Amount of information explains why some regularities are preferred to others, but only within a set of “nonarbitrary” regularities; there are object regularities that are rich in information content, but are considered “arbitrary”, and are not used in generating hypotheses. Which formal property can distinguish between these two sets of regularities?
Analogues of Lusztig's higher order relations for the q-Onsager algebra
