Different Developmental Patterns of Simple Deductive and Probabilistic Inferential Reasoning

By Markovits, Henry; Thompson, Valerie | Memory & Cognition, September 2008 | Go to article overview

Different Developmental Patterns of Simple Deductive and Probabilistic Inferential Reasoning


Markovits, Henry, Thompson, Valerie, Memory & Cognition


In three studies, we examined simple counterexample-based and probabilistic reasoning in children 6, 7, and 9 years of age. In the first study, participants were asked to make conditional (if-then) inferences under both categorical (certain or uncertain) and probabilistic instructions. Results showed that 6-year-olds respond to both forms of inference in similar ways, but whereas probabilistic conditional inferences showed little development over this period, categorical inferences clearly improved between 6 and 7 years of age. An analysis of the children's justifications indicated that performance under categorical instructions was strongly related to counterexample generation at all ages, whereas this was true only for the younger children for inferences under probabilistic instructions. These findings were replicated in a second study, using problems that referred to concrete stimuli with varying probabilities of inference. A third study tested the hypothesis that children confused probability judgments with judgments of confidence and demonstrated a clear dissociation between these two constructs. Overall, these results show that children are capable of accurate conditional inferences under probabilistic instructions at a very early age and that the differentiation between categorical and probabilistic conditional reasoning is clear by at least 9 years of age. These results are globally consistent with dual-process theories but suggest some difficulties for the way that the analytic-heuristic distinction underlying these theories has been conceptualized.

The capacity to make deductive inferences from premises that are assumed to be true is one of the more important abilities characterizing the human cognitive system. A great deal of research has examined the kinds of inferences that are made under standard deductive instructions, which require a dichotomous evaluation of the certainty of a putative conclusion. Studies in which both children and adults have been looked at (e.g., Cummins, 1995; Janveau-Brennan & Markovits, 1999; Thompson, 1994, 2000) have consistently shown a great deal of variation, due to both content and context, in this kind of reasoning. At least two kinds of processes have been posited to explain the observed variation. The first relies on explicit use of counterexamples to judge conclusions as certain or not (Johnson-Laird & Byrne, 1991; Markovits & Barrouillet, 2002; Verschueren, Schaeken, & d'Ydewalle, 2005). Such models assume that retrieval and use of at least one potential counterexample are sufficient to deny a conclusion. The second entails a more probabilistic approach (e.g., Evans, Handley, & Over, 2003; Oaksford, Chater, & Larkin, 2000), which requires an evaluation of the probability of a putative conclusion. This involves some process by which the relative frequency of a potential conclusion is compared with the relative frequency of potential counterexamples. The goal of the present article is to examine the development of these two types of inferential reasoning in young children. Our basic hypothesis is that inferences using judgments of probability emerge early in childhood; explicit inferential reasoning based on explicit use of counterexamples, however, is posited to develop later.

Studies with adults support the hypothesis that when inferences are made on the basis of conditional statements that are familiar to reasoners, counterexample-based inferential reasoning is more demanding than inferential reasoning based on the assessment of probabilities. Verschueren et al. (2005) recently suggested that there are two distinct forms of inferential reasoning, corresponding to two ways of determining whether a putative conclusion is valid. The first relies on likelihood judgments about conclusion plausibility that are fairly intuitive and do not require many cognitive resources. Thus, if the premises suggest that a conclusion is highly likely when compared with potential alternatives that are consistent with the premises (i. …

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