This paper presents a new theory of modal reasoning, i.e. reasoning about what may or may not be the case, and what must or must not be the case. It postulates that individuals construct models of the premises in which they make explicit only what is true. A conclusion is possible if it holds in at least one model, whereas it is necessary if it holds in all the models. The theory makes three predictions, which are corroborated experimentally. First, conclusions (...) correspond to the true, but not the false, components of possibilities. Second, there is a key interaction: it is easier to infer that a situation is possible as opposed to impossible, whereas it is easier to infer that a situation is not necessary as opposed to necessary. Third, individuals make systematic errors of omission and of commission. We contrast the theory with theories based on formal rules. (shrink)

How do people imagine the possibilities in which an assertion would be true and the possibilities in which it would be false? We argue that the mental representation of the meanings of connectives, such as "and", "or", and "if", specify how to construct the true possibilities for simple assertions containing just a single connective. It follows that the false possibilities are constructed by inference from the true possibilities. We report converging evidence supporting this account from four experiments in which the (...) participants had to list the true and the false possibilities for various sorts of assertion. Their systematic errors, response times, and think-aloud protocols corroborated the theory's predictions. Not even true possibilities are immediately available for complex assertions containing two or more different connectives. The task of listing the true possibilities then becomes difficult, and the task of listing the false possibilities almost impossible. (shrink)

'Is there any other point to which you would wish to draw my attention?' 'To the curious incident of the dog in the night-time.' 'The dog did nothing in the night-time.' 'That was the curious incident, ' remarked Sherlock Holmes. The quotation from A. Conan Doyle with which this book begins, is a delightfully appropriate summation of the authors' point of view garnered from their fifteen years of experiments on the psychology of reasoning. Dr. Wason and Dr. Johnson-Laird are intrigued (...) by the extent to which most individuals can be considered naturally rational thinkers. They present here the surprising results of their comprehensive investigations of how humans draw explicit conclusions from evidence. Given a set of assertions, the authors write, to what extent can the individual appreciate all that follows from them by virtue of logic alone, and remain unseduced by plausible, but fallacious conclusions? We are not concerned with whether these assertions are true or false, nor with whether the individual holds them among his beliefs, nor with whether they are sane or silly. At the core of the Psychology of Reasoning is a vigorous discussion that incorporates various illustrations--some of them humorous, all of them fascinating--of the use of reason under a wide variety of different conditions. Particular emphasis is placed on the difficulties involved in dealing with negatively marked information that must be combined and used with other information for reaching conclusions. Thorough treatment is given as well to the search for plausible contexts that will render anomalous or ambiguous statements sensible. The authors have strived to isolate the components ofinference, the basic steps of any kind of deductive activity, in order to determine the psychological processes involved in them. What has been the outcome of this research? Dr. Wason and Dr. Johnson-Laird conclude, our research has suggested that the individual's logical competence may be either enhanced or limited by performance variables. And, of these, content has turned out to be vitally important for revealing, or obscuring structure. At best, we can all think like logicians; at worst, logicians all think like us. (shrink)

The mental model theory postulates that reasoners build models of the situations described in premises, and that these models normally represent only what is true. The theory has an unexpected consequence. It predicts the existence ofillusions in inferences. Certain inferences should have compelling but erroneous conclusions. Two experiments corroborated the occurrence of such illusions in inferences about what is possible from disjunctions of quantified assertions, such as, “at least some of the plastic beads are not red.” Experiment 1 showed that (...) participants erroneously inferred that impossible situations were possible, and that possible situations were impossible, but that they performed well with control problems based on the same premises. Experiment 2 corroborated these findings in inferences from assertions based on dyadic relations, such as, “all the boys played with the girls.”. (shrink)

Four experiments examined the strategies that individuals develop in sentential reasoning. They led to the discovery of five different strategies. According to the theory proposed in the paper, each of the strategies depends on component tactics, which all normal adults possess, and which are based on mental models. Reasoners vary their use of tactics in ways that are not deterministic. This variation leads different individuals to assemble different strategies, which include the construction of incremental diagram corresponding to mental models, and (...) the pursuit of the consequences of a single model step by step. Moreover, the difficulty of a problem (i.e. the number of mental models required by the premises) predisposes reasoners towards certain strategies. Likewise, the sentential connectives in the premises also bias reasoners towards certain strategies, e.g., conditional premises tend to elicit reasoning step by step whereas disjunctive premises tend to elicit incremental diagrams. (shrink)

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. (shrink)

In this study on deduction, the authors argue that people reason by imagining the relevant state of affairs, ie building an internal model of it, formulating a tentative conclusion based on this model and then searching for alternative models.

Lance Rips describes a unified theory of natural deductive reasoning and fashions a working model of deduction, with strong experimental support, that is capable of playing a central role in mental life.