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.

Six experiments explored the hypothesis that the members of categories which are considered most prototypical are those with most attributes in common with other members of the category and least attributes in common with other categories. In probabilistic terms, the hypothesis is that prototypicality is a function of the total cue validity of the attributes of items. In Experiments 1 and 3, subjects listed attributes for members of semantic categories which had been previously rated for degree of prototypicality. High positive (...) correlations were obtained between those ratings and the extent of distribution of an item's attributes among the other items of the category. In Experiments 2 and 4, subjects listed superordinates of category members and listed attributes of members of contrasting categories. Negative correlations were obtained between prototypicality and superordinates other than the category in question and between prototypicality and an item's possession of attributes possessed by members of contrasting categories. Experiments 5 and 6 used artificial categories and showed that family resemblance within categories and lack of overlap of elements with contrasting categories were correlated with ease of learning, reaction time in identifying an item after learning, and rating of prototypicality of an item. It is argued that family resemblance offers an alternative to criterial features in defining categories. (shrink)

People are remarkably smart: They use language, possess complex motor skills, make nontrivial inferences, develop and use scientific theories, make laws, and adapt to complex dynamic environments. Much of this knowledge requires concepts and this study focuses on how people acquire concepts. It is argued that conceptual development progresses from simple perceptual grouping to highly abstract scientific concepts. This proposal of conceptual development has four parts. First, it is argued that categories in the world have different structure. Second, there might (...) be different learning systems that evolved to learn categories of differing structures. Third, these systems exhibit differential maturational course, which affects how categories of different structures are learned in the course of development. And finally, an interaction of these components may result in the developmental transition from perceptual groupings to more abstract concepts. This study reviews a large body of empirical evidence supporting this proposal. (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)

We address the problem of predicting how people will spontaneously divide into groups a set of novel items. This is a process akin to perceptual organization. We therefore employ the simplicity principle from perceptual organization to propose a simplicity model of unconstrained spontaneous grouping. The simplicity model predicts that people would prefer the categories for a set of novel items that provide the simplest encoding of these items. Classification predictions are derived from the model without information either about the number (...) of categories sought or information about the distributional properties of the objects to be classified. These features of the simplicity model distinguish it from other models in unsupervised categorization (where, for example, the number of categories sought is determined via a free parameter), and we discuss how these computational differences are related to differences in modeling objectives. The predictions of the simplicity model are validated in four experiments. We also discuss the significance of simplicity in cognitive modeling more generally. (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)

An alternative account of human concept learning based on an invariance measure of the categorical stimulus is proposed. The categorical invariance model (CIM) characterizes the degree of structural complexity of a Boolean category as a function of its inherent degree of invariance and its cardinality or size. To do this we introduce a mathematical framework based on the notion of a Boolean differential operator on Boolean categories that generates the degrees of invariance (i.e., logical manifold) of the category in respect (...) to its dimensions. Using this framework, we propose that the structural complexity of a Boolean category is indirectly proportional to its degree of categorical invariance and directly proportional to its cardinality or size. Consequently, complexity and invariance notions are formally unified to account for concept learning difficulty. Beyond developing the above unifying mathematical framework, the CIM is significant in that: (1) it precisely predicts the key learning difficulty ordering of the SHJ [Shepard, R. N., Hovland, C. L.,&Jenkins, H. M. (1961). Learning and memorization of classifications. Psychological Monographs: General and Applied, 75(13), 1-42] Boolean category types consisting of three binary dimensions and four positive examples; (2) it is, in general, a good quantitative predictor of the degree of learning difficulty of a large class of categories (in particular, the 41 category types studied by Feldman [Feldman, J. (2000). Minimization of Boolean complexity in human concept learning. Nature, 407, 630-633]); (3) it is, in general, a good quantitative predictor of parity effects for this large class of categories; (4) it does all of the above without free parameters; and (5) it is cognitively plausible (e.g., cognitively tractable). (shrink)

What is the relationship between the degree of learning difficulty of a Boolean concept (i.e., a category defined by logical rules expressed in terms of Boolean operators) and the complexity of its logical description? Feldman [(2000). Minimization of Boolean complexity in human concept learning. Nature, 407(October), 630–633] investigated this question experimentally by defining the complexity of a Boolean formula (that logically describes a concept) as the length of the shortest formula logically equivalent to it. Using this measure as the independent (...) variable in his experiment, he concludes that in general, the subjective difficulty of learning a Boolean concept is well predicted by Boolean complexity. Moreover, he claims that one of the landmark results and benchmarks in the human concept learning literature, the Shepard, Hovland, and Jenkins learning difficulty ordering, is precisely predicted by this hypothesis. However, in what follows, we introduce a heuristic procedure for reducing Boolean formulae, based in part on the well-established minimization technique from Boolean algebra known as the Quine–McCluskey (QM) method, which when applied to the SHJ Boolean concept types reveals that some of their complexity values are notably different from the approximate values obtained by Feldman. Furthermore, using the complexity values for these simpler expressions fails to predict the correct empirical difficulty ordering of the SHJ concept types. Motivated by these findings, this note includes a brief tutorial on the QM method and concludes with a brief discussion on some of the challenges facing the complexity hypothesis. (shrink)