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 new 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.
The authors outline a theory of conditionals of the form If A then C and If A then possibly C. The 2 sorts of conditional have separate core meanings that refer to sets of possibilities. Knowledge, pragmatics, and semantics can modulate these meanings. Modulation can add information about temporal and other relations between antecedent and consequent. It can also prevent the construction of possibilities to yield 10 distinct sets of possibilities to which conditionals can refer. The mental representation of a (...) conditional normally makes explicit only the possibilities in which its antecedent is true, yielding other possibilities implicitly. Reasoners tend to focus on the explicit possibilities. The theory predicts the major phenomena of understanding and reasoning with conditionals. (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)
Inferences about spatial, temporal, and other relations are ubiquitous. This article presents a novel model-based theory of such reasoning. The theory depends on 5 principles. The structure of mental models is iconic as far as possible. The logical consequences of relations emerge from models constructed from the meanings of the relations and from knowledge. Individuals tend to construct only a single, typical model. They spontaneously develop their own strategies for relational reasoning. Regardless of strategy, the difficulty of an inference depends (...) on the process of integration of the information from separate premises, the number of entities that have to be integrated to form a model, and the depth of the relation. The article describes computer implementations of the theory and presents experimental results corroborating its main principle. (shrink)
This paper replies to Politzer’s ( 2007 ) criticisms of the mental model theory of conditionals. It argues that the theory provides a correct account of negation of conditionals, that it does not provide a truth-functional account of their meaning, though it predicts that certain interpretations of conditionals yield acceptable versions of the ‘paradoxes’ of material implication, and that it postulates three main strategies for estimating the probabilities of conditionals.
The communicative theory of emotions postulates that emotions are communications both within the brain and between individuals. Basic emotions owe their evolutionary origins to social mammals, and they enable human beings to use repertoires of mental resources appropriate to recurring and distinctive kinds of events. These emotions also enable them to cooperate with other individuals, to compete with them, and to disengage from them. The human system of emotions has also grafted onto basic emotions propositional contents about the cause of (...) the emotion, the self, and other matters. Complex emotions always contain such contents, whereas basic emotions can be experienced without them. This article explains the role of basic emotions in social relationships, their effects on reasoning, and their pathology in psychological illness, such as depression and obsessive-compulsive disorder. (shrink)
The mental model theory postulates that reasoners build models of the situations described in premises. A conclusion is possible if it holds in at least one model of the premises; it is probable if it holds in most of the models; and it is necessary if it holds in all of the models. The theory also postulates that reasoners represent as little information as possible in explicit models and, in particular, that they represent only information about what is true. One (...) unexpected consequence of this assumption is that there should be a category of illusory inferences: they will have conclusions that seem obvious, but that are wholly erroneous. Experiment 1 established the existence of such illusory inferences about probabilities. Overall, 88% of the intelligent adult subjects chose as more probable an outcome that was impossible for at least one of the illusory problems. Experiment 2 corroborated the phenomenon and showed that illusory inferences include a wide variety of problems. Finally, the paper argues that current theories based on formal rules of inference are unlikely to be able to explain the illusions. (shrink)
We report three experimental studies of reasoning with double conditionals, i.e. problems based on premises of the form: If A then B. If B then C. where A, B, and C, describe everyday events. We manipulated both the logical structure of the problems, using all four possible arrangements (or “figures” of their constituents, A, B, and C, and the believability of the two salient conditional conclusions that might follow from them, i.e. If A then C, or If C then A. (...) The experiments showed that with figures for which there was a valid conclusion, the participants more often, and more rapidly, drew the valid conclusion when it was believable than when it was unbelievable. With figures for which there were no valid conclusions, the participants tended to draw whichever of the two conclusions was believable. These results were predicted by the theory that reasoning depends on constructing mental models of the premises. (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)
This chapter describes the main accounts of deductive competence, which explain what is computed in carrying out deductions. It argues that people have a modicum of competence, which is useful in daily life and a prerequisite for acquiring logical expertise. It outlines the three main sorts of theory of deductive performance, which explain how people make deductions: They rely on factual knowledge, formal rules, or mental models. It reviews recent experimental studies of deductive reasoning in order to help readers to (...) assess these theories of performance. (shrink)
This paper reports three studies of temporal reasoning. A problem of the following sort, where the letters denote common everyday events: A happens before B. C happens before B. D happens while B. E happens while C. What is the relation between D and EEfficacylls for at least two alternative models to be constructed in order to give the right answer for the right reason. However, the first premise is irrelevant to this answer, and so if reasoners were to ignore (...) it, then they would need to construct only one model. Experiment 1 showed that one-model problems were answered faster and more accurately than multiple-model problems. When the question preceded the premises in the statement of the multiple-model problems there was a slight tendency for the latencies of response to speed up in the predicted way. Experiment 2 modified the procedure, in part by using practice problems with many irrelevant premises, so that reasoners might grasp the advantage of ignoring them. Its results showed that when the premises preceded the question, the multiple-model problems were significantly harder than one-model problems. But when the question was presented first, the difference was significantly reduced in line with the theory's prediction. Experiment 3 used only problems with valid conclusions, and so the construction of multiple models was never necessary. However, there was still a significant difference between one-model problems and multiple-model problems. (shrink)
This second volume in the Counterpoints Series focuses on alternative models of visual-spatial processing in human cognition. The editors provide a historical and theoretical introduction and offer ideas about directions and new research designs.
Abstract Theories of induction in psychology and artificial intelligence assume that the process leads from observation and knowledge to the formulation of linguistic conjectures. This paper proposes instead that the process yields mental models of phenomena. It uses this hypothesis to distinguish between deduction, induction, and creative forms of thought. It shows how models could underlie inductions about specific matters. In the domain of linguistic conjectures, there are many possible inductive generalizations of a conjecture. In the domain of models, however, (...) generalization calls for only a single operation: the addition of information to a model. If the information to be added is inconsistent with the model, then it eliminates the model as false: this operation suffices for all generalizations in a Boolean domain. Otherwise, the information that is added may have effects equivalent (a) to the replacement of an existential quantifier by a universal quantifier, or (b) to the promotion of an existential quantifier from inside to outside the scope of a universal quantifier. The latter operation is novel, and does not seem to have been used in any linguistic theory of induction. Finally, the paper describes a set of constraints on human induction, and outlines the evidence in favor of a model theory of induction. (shrink)
Two experiments investigated inferences based on suppositions. In Experiment 1, the subjects decided whether suppositions about individuals' veracity were consistent with their assertions—for example, whether the supposition “Ann is telling the truth and Beth is telling a lie”, is consistent with the premises: “Ann asserts: I am telling the truth and Beth is telling the truth. Beth asserts: Ann is telling the truth”. It showed that these inferences are more difficult than ones based on factual premises: “Ann asserts: I live (...) in Dublin and Beth lives in Dublin”. There was no difference between problems about truthtellers and liars, who always told the truth or always lied, and normals, who sometimes told the truth and sometimes lied. In Experiment 2, the subjects made inferences about factual matters set in three contexts: a truth-inducing context in which friends confided their personality characteristics, a lie-inducing context in which business rivals advertised their products, and a neutral context in which computers printed their program characteristics. Given the supposition that the individuals were lying, it was more difficult to make inferences in a truth-inducing context than in the other two contexts. We discuss the implications of our results for everyday reasoning from suppositions, and for theories of reasoning based on models or inference rules. (shrink)
This paper explores the ways in which Wilbur and Orville Wright thought as they tackled the problem of designing and constructing a heavier-than-air craft that would fly under its own power and under their control. It argues that their use of analogy and their use of knowledge in diagnostic reasoning lies outside the scope of current psychological theories and their computer implementations. They used analogies based on mental models of one system, such as the wings, to help them to develop (...) theories of another system, such as the propellers. They were also skilled reasoners, who were adept at finding counterexamples to arguments. (shrink)