People reject ‘paradoxical’ inferences, such as: Luisa didn't play music; therefore, if Luisa played soccer, then she didn't play music. For some theorists, they are invalid for everyday conditionals, but valid in logic. The theory of mental models implies that they are valid, but unacceptable because the conclusion refers to a possibility inconsistent with the premise. Hence, individuals should accept them if the conclusions refer only to possibilities consistent with the premises: Luisa didn't play soccer; therefore, if Luisa played a (...) game then she didn't play soccer. Two experiments corroborated this prediction for three sorts of ‘paradox’, including a disjunctive paradox. (shrink)

People reject ‘paradoxical’ inferences, such as: Luisa didn't play music; therefore, if Luisa played soccer, then she didn't play music. For some theorists, they are invalid for everyday conditionals, but valid in logic. The theory of mental models implies that they are valid, but unacceptable because the conclusion refers to a possibility inconsistent with the premise. Hence, individuals should accept them if the conclusions refer only to possibilities consistent with the premises: Luisa didn't play soccer; therefore, if Luisa played a (...) game then she didn't play soccer. Two experiments corroborated this prediction for three sorts of ‘paradox’, including a disjunctive paradox. (shrink)

The theory of mental models and its computer implementations have led to crucial experiments showing that no standard logic—the sentential calculus and all logics that include it—can underlie human reasoning. The theory replaces the logical concept of validity (the conclusion is true in all cases in which the premises are true) with necessity (conclusions describe no more than possibilities to which the premises refer). Many inferences are both necessary and valid. But experiments show that individuals make necessary inferences that are (...) invalid, e.g., Few people ate steak or sole; therefore, few people ate steak. Other crucial experiments show that individuals reject inferences that are not necessary but valid, e.g., He had the anesthetic or felt pain, but not both; therefore, he had the anesthetic or felt pain, or both. Nothing in logic can justify the rejection of a valid inference: a denial of its conclusion is inconsistent with its premises, and inconsistencies yield valid inferences of any conclusions whatsoever including the one denied. So inconsistencies are catastrophic in logic. In contrast, the model theory treats all inferences as defeasible (nonmonotonic), and inconsistencies have the null model, which yields only the null model in conjunction with any other premises. So inconsistences are local. Which allows truth values in natural languages to be much richer than those that occur in the semantics of standard logics; and individuals verify assertions on the basis of both facts and possibilities that did not occur. (shrink)

This paper reviews current psychological theories of syllogistic inference and establishes that despite their various merits they all contain deficiencies as theories of performance. It presents the results of two experiments, one using syllogisms and the other using three-term series problems, designed to elucidate how the arrangement of terms within the premises affects performance. These data are used in the construction of a theory based on the hypothesis that reasoners construct mental models of the premises, formulate informative conclusions about the (...) relations in the model, and search for alternative models that are counterexamples to these conclusions. This theory, which has been implemented in several computer programs, predicts that two principal factors should affect performance: the figure of the premises, and the number of models that they call for. These predictions were confirmed by a third experiment. Dans cet article sont passées en revue les théories psychologiques du traitement des syllogismes. On établit qu'en dépit de leurs mérites variés toutes sont en défaut en tant que théories de la performance. On présente les résultats de deux expériences, une utilisant des syllogismes et l'autre des problémes avec des séries de trois termes conçues pour élucider comment l'arrangement des termes dans les premises affecte la performance. Ces données sont utilisées pour construire une théorie fondée sur l'hypothése que les gens construisent des modèles mentaux des premises, formulent des conclusions explicites sur les relations dans le modèle et cherchent des modèles qui seraient des contre-exemples pour leurs conclusions. Cette théorie, utilisée dans plusieurs programmes d'ordinateur, prédit que deux principaux facteurs affectent la performance: la figure des premises et le nombre de; modèles qu'ils mettent en jeu. Cette prédiction est confirmée dans les trois expériences. (shrink)

This paper argues that mental models of discourse are key in any theory of the interpretation of definite descriptions. It considers both referential and attributive uses of such descriptions, in the sense introduced by Donnellan.

This paper describes a semantics for modal terms such as can and may that is intended to model the mental representation of their meaning. The basic assumption of the theory is that the evaluation of a modal assertion involves an attempted mental construction of a specified alternative to a given situation rather than the separate evaluation of each member of a set of possible alternatives as would be required by a “possible worlds” semantics. The theory leads to the conclusion that, (...) contrary to what is often assumed, modal auxiliary verbs are unambiguous. (shrink)

Given a basic conditional of the form, If A then C, individuals usually list three cases as possible: A and C, not‐A and not‐C, not‐A and C. This result corroborates the theory of mental models. By contrast, individuals often judge that the conditional is true only in the case of A and C, and that cases of not‐A are irrelevant to its truth or falsity. This result corroborates other theories of conditionals. To resolve the discrepancy, we devised two new tasks: (...) the “collective” truth task, in which participants judged whether sets of assertions about a specific individual, such as: If A then C, not‐A, C, could all be true at the same time; and one in which participants judged the truth of conditional predictions about specific future events. The results consistently matched the three possibilities, thereby corroborating the model theory. They also showed a massive violation of the probability calculus in estimates of the probabilities of the four cases in the partition of conditionals (A and C, A and not‐C, not‐A and C, and not‐A and not‐C), which summed to over 200%. (shrink)

We resolve the two problems that Hardman raises. The first problem arises from a misunderstanding: the crucial distinction is between one-model and multiple-model problems. The second problem illuminates a deeper principle: conclusions depend on the procedures for interpreting models. We describe an algorithm that obviates the problem and empirical work that reveals a new view of syllogistic reasoning.

Some philosophers argue that the principles of human reasoning are impeccable, and that mistakes are no more than momentary lapses in “information processing”. This article makes a case to the contrary. It shows that human reasoners commit systematic fallacies. The theory of mental models predicts these errors. It postulates that individuals construct mental models of the possibilities to which the premises of an inference refer. But, their models usually represent what is true in a possibility, not what is false. This (...) procedure reduces the load on working memory, and for the most part it yields valid inferences. However, as a computer program implementing the theory revealed, it leads to fallacious conclusions for certain inferences—those for which it is crucial to represent what is false in a possibility. Experiments demonstrate the variety of these fallacies and contrast them with control problems, which reasoners tend to get right. The fallacies can be compelling illusions, and they occur in reasoning based on sentential connectives such as “if” and “or”, quantifiers such as “all the artists” and “some of the artists”, on deontic relations such as “permitted” and “obligated”, and causal relations such as “causes” and “allows”. After we have reviewed the principal results, we consider the potential for alternative accounts to explain these illusory inferences. And we show how the illusions illuminate the nature of human rationality. (shrink)

This paper describes Peirce's systems of logic diagrams, focusing on the so-called ''existential'' graphs, which are equivalent to the first-order predicate calculus. It analyses their implications for the nature of mental representations, particularly mental models with which they have many characteristics in common. The graphs are intended to be iconic, i.e., to have a structure analogous to the structure of what they represent. They have emergent logical consequences and a single graph can capture all the different ways in which a (...) possibility can occur. Mental models share these properties. But, as the graphs show, certain aspects of propositions cannot be represented in an iconic or visualisable way. They include negation, and the representation of possibilities qua possibilities, which both require representations that do not depend on a perceptual modality. Peirce took his graphs to reveal the fundamental operations of reasoning, and the paper concludes with an analysis of different hypotheses about these operations. (shrink)

Knauff and Gazzo Castañeda (this issue) critique the "new paradigm" – a framework that replaces logic with probabilities – on the grounds that there existed no "old” paradigm for it to supplant. Their position is supported by the large numbers of theories that theorists developed to explain the Wason selection task, syllogisms, and other tasks. We propose some measures to inhibit such facile theorizing, which threatens the viability of cognitive science. We show that robust results exist contrary to the new (...) paradigm, and that it is unable to account for other results. (shrink)

Sudoku puzzles, which are popular worldwide, require individuals to infer the missing digits in a 9 9 array according to the general rule that every digit from 1 to 9 must occur once in each row, in each column, and in each of the 3-by-3 boxes in the array. We present a theory of how individuals solve these puzzles. It postulates that they rely solely on pure deductions, and that they spontaneously acquire various deductive tactics, which differ in their difficulty (...) depending on their “relational complexity”, i.e., the number of constraints on which they depend. A major strategic shift is necessary to acquire tactics for more difficult puzzles: solvers have to keep track of possible digits in a cell. We report three experiments corroborating this theory. We also discuss their implications for theories of reasoning that downplay the role of deduction in everyday reasoning. (shrink)

Good reasoning can lead to success; bad reasoning can lead to catastrophe. Yet it's not obvious how we reason, and why we make mistakes. This book by one of the pioneers of the field, Philip Johnson-Laird, looks at the mental processes that underlie our reasoning. It provides the most accessible account yet of the science of reasoning.

Van der Henst argues that the theory of mental models lacks a pragmatic component. He fills the gap with the notion that reasoners draw the most relevant conclusions. We agree, but argue that theories need an element of “nondeterminism.” It is often impossible to predict either what will be most relevant or which particular conclusion an individual will draw.

This paper outlines a theory and computer implementation of causal meanings and reasoning. The meanings depend on possibilities, and there are four weak causal relations: A causes B, A prevents B, A allows B, and A allows not‐B, and two stronger relations of cause and prevention. Thus, A causes B corresponds to three possibilities: A and B, not‐A and B, and not‐A and not‐B, with the temporal constraint that B does not precede A; and the stronger relation conveys only the (...) first and last of these possibilities. Individuals represent these relations in mental models of what is true in the various possibilities. The theory predicts a number of phenomena, and, contrary to many accounts, it implies that the meaning of causation is not probabilistic, differs from the meaning of enabling conditions, and does not depend on causal powers or mechanisms. The theory also implies that causal deductions do not depend on schemas or rules. (shrink)

In this paper we investigate the locus of believability effects in syllogistic reasoning. We identify three points in the reasoning process at which such effects could occur: the initial interpretation of premises, the examination of alternative representations of them (in all of which any valid conclusion must be true), and the “filtering” of putative conclusions. The effect of beliefs at the first of these loci is well established. In this paper we report three experiments that examine whether beliefs have an (...) effect at the other two loci. In experiments 1 and 2 subjects drew their own conclusions from syllogisms that suggested believable or unbelievable ones. In the third experiment they evaluated conclusions that were presented to them. The data show that beliefs both affect the examination of alternative models and act as a filter on putative conclusions. We conclude by showing how some types of problem and some problem contents make the existence of alternative models more obvious than others. (shrink)

(2013). The processes of inference. Argument & Computation: Vol. 4, Formal Models of Reasoning in Cognitive Psychology, pp. 4-20. doi: 10.1080/19462166.2012.674060.