Acta Psychologica Sinica

Abstract

Inductive reasoning is an activity of the mind that takes one from the observed to the unobserved. For category-based induction, there are the following robust experimental results. For inference from a single premise, (1) similarity between the premise and conclusion categories promotes induction, (2) typicality of the premise category promotes induction, (3) homogeneity of the conclusion category promotes induction, (4) switching the premise and conclusion categories can lead to arguments with different inductive strength (i.e., an asymmetrical phenomenon), and (5) inductive strength increases with connection strength between induction features and relevant features. For inference from multiple premises, (6) a greater number of premises promotes induction, and (7) a greater diversity of premises promotes induction. Moreover, (8) contents of induction features affect inductive inference.

For these phenomena, there are four major descriptive explanations: the similarity-coverage model (Osherson, et al., 1990), the feature-based induction model (Sloman, 1993), the relevance theory of induction (Medin, 2003), and the relevance similarity model of feature induction (Wang, 2006). None of these explanations can explain all the aforementioned inductive phenomena. Either of the similarity-coverage model or the feature-based induction model can at most explain items (1), (2), (4), (6), and (7) above. These models are limited because they do not embody the essence of the mostly general inductive phenomena inherent in inductive reasoning — according to some category or feature sample relevant to an induction feature — to infer the possibility that a conclusion category has the induction feature. The author proposes a sampling theory of inductive reasoning that argues human inductive reasoning can embody and conform to the essence. The sampling theory can explain (1), (2), (3), (4), (6), and (7) of the aforementioned inductive phenomena.

Three major theories (the similarity-coverage model, the feature-based induction model, and the sampling theory) all seem to be able to explain phenomenon (4), but there has thus far been no discriminative test for these three theories. Two experiments were designed to serve as discriminative tests of the three theories; they had similar designs that used artificial categories as premise and conclusion categories. For example, the following two induction problems formed a pair comparison.

Induction 1:
It was formerly known:
Insect A has features a, b, c, d, e, f.
Insect B has features a, b, c, d, e, g, h, k, l, m.
Now it is found that insect A has feature x. What is the possibility that insect B has feature x?

Induction 2:
It was formerly known:
Insect B has features a, b, c, d, e, g, h, k, l, m.
Insect A has features a, b, c, d, e, f.
Now it is found that insect B has feature x. What is the possibility that insect A has feature x?

For these two induction problems, there was a switch between the premise and conclusion categories. The three theories made different predictions for the size-order of the inductive strengths of the two inductions. The similarity-coverage model predicted that there would be no difference in inductive strength between the two inductions, because the similarity of the two kinds of insects was identical in the two inductions. The feature-based induction model predicted that the inductive strength of induction 2 would be larger than that of induction 1, according to the feature coverage of the premise categories over the conclusion categories. The sampling theory predicted that the inductive strength of induction 1 would be larger than that of induction 2, according to the proportion of features in the premise categories that transfer from premise categories to conclusion categories. Therefore, the three theories can be discriminatively tested by examining participants’ inductive strengths would conform to which prediction.

The results of the four paired comparisons in each experiment consistently conformed to the predictions made by the sampling theory. The results consistently support the sampling theory rather than the other two explanations. The other two explanations essentially cannot explain the asymmetrical phenomena in the two experiments. Therefore, the sampling theory has a greater scope of explanation than do the other descriptive explanations of inductive reasoning.

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