This article outlines a theory of naive probability. According to the theory, individuals who are unfamiliar with the probability calculus can infer the probabilities of events in an extensional way: They construct mental models of what is true in the various possibilities. Each model represents an equiprobable alternative unless individuals have beliefs to the contrary, in which case some models will have higher probabilities than others. The probability of an event depends on the proportion of models in which it occurs. The theory predicts several phenomena of reasoning about absolute probabilities, including typical biases. It correctly predicts certain cognitive illusions in inferences about relative probabilities. It accommodates reasoning based on numerical premises, and it explains how naive reasoners can infer posterior probabilities without relying on Bayes's theorem. Finally, it dispels some common misconceptions of probabilistic reasoning.

An experimoiit was performed to determine whether the use of realistic materials mould improve performance in a deceptive reasoning problem. The task involved selecting from a set of envelopes those which, if they were turned ovor, could violate a given rule. The rulo concerned either a realistic relation ('if a letter is sealed, then it has a 50 lire stamp on it') or else an arbitrary relation between symbols ('if a letter has an A on one side, then i t has a 3 on the other side'). Twenty-two of the 24 subjects made at least one correct answer with the realistic material but only seven of them did so with the symbolic materials. The verbal formulation of the rule was also varied but yielded only a marginal interaction with tho main variable. It is argued that the critical factor is the intrinsic connexion betweon items rather than their specific nature.It is a w-ell-established fact that the content of a problem may have a significant effect upon insight into its underlying structure. Perhaps the clearest demonstration of this phenomenon in a purely deductive task is Wilkins's (1928) classic study of syllogistic inference. She discovered that problems with a familiar everyday content were generally easier than those with a purely symbolic or totally unfamiliar content : her subjects committed fewer fallacies even though the familiarity of the material provided no cue to what was, or was not, the valid conclusion. To anyone approaching thinking from a strictly formal point of view (such as the logically oriented psychologist or genetic epistemologist) this finding is both surprising and perplexing because in making a deduction the same mental operations are presumed to be carried out regardless of content. Hence, why should it be harder to execute them with one sort of material than with another? Our investigation was designed to re-examine the phenomenon and to try to answer this question.The particular deductive problem that we chose to study was one developed by Wason (1068). The subject is presented with the four cards shown in Fig. 1, together with the following rule : If a card has a n A on one side, then it has a 3 on the other side.He knows that each card has a letter on one side and a number on the other side; and his task is to choose just those cards which it is necessary to turn over in order to discover whether the rule is true or false. This is an extraordinarily deceptive problem even for the most intelligent of sub-

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Our principal hypothesis is that reasoning and decision making are alike in that they both depend on the construction of mental models, and so they should both give rise to similar phenomena.In this paper, we consider one such phenomenon, which we refer to as "focussing": individuals are likely to restrict their thoughts to what is explicitly represented in their models. We show that focussing occurs in four domains. First, individuals fail to draw inferences in the modus tollens form: if p then q, not-q, therefore not-p, because they focus on their initial models of the conditional, which make explicit only the case where the antecedent (p) and consequent (q) occur. Second, in Wason's selection task, they similarly tend to select only those cards that are explicitly represented in their initial models of the conditional rule. Third, their requests for information in order to enable them to make a decision about whether or not to carry out a certain action are focussed on the action to the exclusion of alternatives to it. In each of these cases, we show how the focussing bias can be reduced by certain experimental manipulations. Finally, in counterfactual reasoning, focussing underlies individuals' attempts to imagine an alternative scenario that avoids an unfortunate ending to a story.

This article presents a theory of how individuals reason from inconsistency to consistency. The theory is based on 3 main principles. First, individuals try to construct a single mental model of a possibility that satisfies a current set of propositions, and if the task is impossible, they infer that the set is inconsistent. Second, when an inconsistency arises from an incontrovertible fact, they retract any singularly dubious proposition or any proposition that is inconsistent with the fact; otherwise, they retract whichever proposition mismatches the fact. A mismatch can arise from a proposition that has only mental models that conflict with the fact or fail to represent it. Third, individuals use their causal knowledge-in the form of models of possibilities-to create explanations of what led to the inconsistency. A computer program implements the theory, and experimental results support each of its principles.

Reasoners succumb to predictable illusions in evaluating whether sets of assertions are consistent. We report two studies of this computationally intractable task of "satisfiability." The results show that as the number of possibilities compatible with the assertions increases, the difficulty of the task increases, and that reasoners represent what is true according to assertions, not what is false. This procedure avoids overloading memory, but it yields illusions of consistency and of inconsistency. These illusions modify our picture of human rationality.

One hundred and fifty‐five participants had to solve a set of 2–4–6 like reasoning problems (Wason, 1960), in which they were told which hypothesis a majority (or a minority) proposed, as well as which example was used for the test. In a 2 × 2 design, participants were also told that the problems allowed either one single correct answer or several possible answers. Results show that, when the source is a majority and the problem allows one single answer, most participants adopt the source's hypothesis and use confirmatory testing. On the contrary, it is when the source is a minority and the problem allows several answers that most participants give alternative hypotheses and use disconfirmation.

This article reports three experiments that deal with the source of the difficulty of Wason's (1977) THOG problem. The solution of this problem demands both the postulation of hypotheses and a combinatorial analysis of their consequences. Experiment 1 showed that the generation of the hypotheses is not in itself sufficient to solve the problem. Experiment 2 showed that a version presenting a plausible context for separating the level of data from that of hypotheses produced a better performance than both the original abstract version and a thematic version lacking the plausible context separating the levels. Experiment 3 gave evidence that this context can produce facilitation even with the geometric material of the classic version. This experiment also showed that a pictorial presentation of data and a verbal presentation of hypotheses affect performance negatively. The results demonstrate the role of problem representation in problem solving, and, in particular, the role of homogeneity in representing data and hypotheses in hypothetico-deductive reasoning.