Keith Holyoak and Paul Thagard provide a unified, comprehensive account of the diverse operations and applications of analogy, including problem solving, ...

Over the last quarter century, the dominant tendency in comparative cognitive psychology has been to emphasize the similarities between human and nonhuman minds and to downplay the differences as (Darwin 1871). In the present target article, we argue that Darwin was mistaken: the profound biological continuity between human and nonhuman animals masks an equally profound discontinuity between human and nonhuman minds. To wit, there is a significant discontinuity in the degree to which human and nonhuman animals are able to approximate (...) the higher-order, systematic, relational capabilities of a physical symbol system (PSS) (Newell 1980). We show that this symbolic-relational discontinuity pervades nearly every domain of cognition and runs much deeper than even the spectacular scaffolding provided by language or culture alone can explain. We propose a representational-level specification as to where human and nonhuman animals' abilities to approximate a PSS are similar and where they differ. We conclude by suggesting that recent symbolic-connectionist models of cognition shed new light on the mechanisms that underlie the gap between human and nonhuman minds. (shrink)

We propose that people typically reason about realistic situations using neither content-free syntactic inference rules nor representations of specific experiences. Rather, people reason using knowledge structures that we term pragmatic reasoning schemas, which are generalized sets of rules defined in relation to classes of goals. Three experiments examined the impact of a “permission schema” on deductive reasoning. Experiment 1 demonstrated that by evoking the permission schema it is possible to facilitate performance in Wason's selection paradigm for subjects who have had (...) no experience with the specific content of the problems. Experiment 2 showed that a selection problem worded in terms of an abstract permission elicited better performance than one worded in terms of a concrete but arbitrary situation, providing evidence for an abstract permission schema that is free of domain-specific content. Experiment 3 provided evidence that evocation of a permission schema affects not only tasks requiring procedural knowledge, but also a linguistic rephrasing task requiring declarative knowledge. In particular, statements in the form if p then q were rephrased into the form p only if q with greater frequency for permission than for arbitrary statements, and rephrasings of permission statements produced a pattern of introduction of modals totally unlike that observed for arbitrary conditional statements. Other pragmatic schemas, such as “causal” and “evidence” schemas can account for both linguistic and reasoning phenomena that alternative hypotheses fail to explain. (shrink)

We examine the use of analogy in human thinking from the perspective of a multiconstraint theory, which postulates three basic types of constraints: similarity, structure and purpose. The operation of these constraints is apparent in both laboratory experiments on analogy and in naturalistic settings, including politics, psychotherapy, and scientific research. We sketch how the multiconstraint theory can be implemented in detailed computational simulations of the analogical human mind.

We created paired moral dilemmas with minimal contrasts in wording, a research strategy that has been advocated as a way to empirically establish principles operative in a domain‐specific moral psychology. However, the candidate “principles” we tested were not derived from work in moral philosophy, but rather from work in the areas of consumer choice and risk perception. Participants were paradoxically less likely to choose an action that sacrifices one life to save others when they were asked to provide more reasons (...) for doing so (Experiment 1), and their willingness to sacrifice lives depended not only on how many lives would be saved, but on the number of lives at risk (Experiment 2). The latter effect was also found in a within‐subjects design (Experiment 3). These findings suggest caution in the use of artificial dilemmas as a key testbed for revealing principled bases for moral judgment. (shrink)

We report a study examining the role of linguistic context in modulating the influences of individual differences in fluid and crystalized intelligence on comprehension of literary metaphors. Three...

Theories of skill acquisition have made radically different predictions about the role of general problem‐solving methods in acquiring rules that promote effective transfer to new problems. Under one view, methods that focus on reaching specific goals, such as means‐ends analysis, are assumed to provide the basis for efficient knowledge compilation (Anderson, 1987), whereas under an alternative view such methods are believed to disrupt rule induction (Sweller, 1988). We suggest that the role of general methods in learning varies with both the (...) specificity of the problem solver's goal and the systematicity of the strategies used for testing hypotheses about rules. In the absence of a specific goal people are more likely to use a rule‐induction learning strategy, whereas provision of a specific goal fosters use of difference reduction, which tends to be a non‐rule‐induction strategy. We performed two experiments to investigate the impact of goal specificity and systematicity of rule‐induction strategies in learning and transfer within a complex dynamic system. The results of Experiment 1 indicated that during free exploration of a problem space, greater learning occurred if participants adopted more systematic strategies for rule induction, and that participants come to favor such strategies. Experiment 2 revealed that participants who were provided with a specific goal performed well on the initial problem but were impaired on a transfer test using a similar problem with a different goal. Instruction on a systematic rule‐induction strategy facilitated solution for both the initial and transfer problems, but participants' use of this strategy declined if they had a specific goal. Our results support Sweller's (1988) proposal that general problemsolving methods applied to a specific goal foster acquisition of knowledge about an isolated solution path but do not provide an effective way of learning the overall structure of a problem space. We interpret these results in terms of dualspace theories of search through problem space. (shrink)

The effect of state anxiety on analogical reasoning was investigated by examining qualitative differences in mapping performance between anxious and non-anxious individuals reasoning about pictorial analogies. The working-memory restriction theory of anxiety, coupled with theories of analogy that link complexity of mapping with working-memory capacity, predicts that high anxiety will impair the ability to find correspondences based on relations between multiple objects relative to correspondences based on overlap of attributes between individual objects. Anxiety was induced in one condition by a (...) stressful speeded subtraction task administered prior to the analogy task. Anxious participants produced fewer relational responses and more attribute responses than did non-anxious participants, both in the absence of explicit instructions to find relational mappings (Experiment 1) and after receiving such instructions (Experiment 2). The findings support the postulated links among anxiety, working memory, and the ability to perform complex analogical mapping. (shrink)

Theories of analogical reasoning have viewed relational structure as the dominant determinant of analogical mapping and inference, while assigning lesser importance to similarity between individual objects. An experiment is reported in which these two sources of constraints on analogy are placed in competition under conditions of high relational complexity. Results demonstrate equal importance for relational structure and object similarity, both in analogical mapping and in inference generation. The human data were successfully simulated using a computational analogy model (LISA) that treats (...) both relational correspondences and object similarity as soft constraints that operate within a limited-capacity working memory; but not with a model (SME) that treats relational structure as pre-eminent. (shrink)

Research on language processing has shown that the disruption of conceptual integration gives rise to specific patterns of event-related brain potentials —N400 and P600 effects. Here, we report similar ERP effects when adults performed cross-domain conceptual integration of analogous semantic and mathematical relations. In a problem-solving task, when participants generated labeled answers to semantically aligned and misaligned arithmetic problems, the second object label in misaligned problems yielded an N400 effect for addition problems. In a verification task, when participants judged arithmetically (...) correct but semantically misaligned problem sentences to be “unacceptable,” the second object label in misaligned sentences elicited a P600 effect. Thus, depending on task constraints, misaligned problems can show either of two ERP signatures of conceptual disruption. These results show that well-educated adults can integrate mathematical and semantic relations on the rapid timescale of within-domain ERP effects by a process akin to analogical mapping. (shrink)

This article addresses the ability of Parallel Distributed Processing (PDP) networks to generate stagewise cognitive development in accordance with Piaget's theory of cognitive epigenesis. We carried out a replication study of the simulation experiments by McClelland (1989) and McClelland and Jenkins (1991) in which a PDP network learns to solve balance scale problems. In objective tests motivated from catastrophe theory, a mathematical theory of transitions in epigenetical systems, no evidence for stage transitions in network performance was found. It is concluded (...) that PDP networks lack the ability to recover the positive outcomes of analogous catastrophe analyses of real cognitive developmental data. In an attempt to further characterize the learning behaviour of PDP networks, we carried out a second simulation study using the discrimination‐shift paradigm. The results thus obtained indicate that PDP learning is compatible with the learning of stimulus‐response relationships, not with the acquisition of mediating rules such as conceived in (neo‐)Piagetian theory. In closing, we speculate about the feasibility of simulating stagewise development with alternative network architectures. (shrink)

Why might it be beneficial for adults to process fractions componentially? Recent research has shown that college-educated adults can capitalize on the bipartite structure of the fraction notation, performing more successfully with fractions than with decimals in relational tasks, notably analogical reasoning. This study examined patterns of relational priming for problems with fractions in a task that required arithmetic computations. College students were asked to judge whether or not multiplication equations involving fractions were correct. Some equations served as structurally inverse (...) primes for the equation that immediately followed it. Students with relatively high math ability showed relational priming both with and without high perceptual similarity. Students with relatively low math ability also showed priming, but only when the structurally inverse equation pairs were supported by high perceptual similarity between numbers. Several additional experiments established boundary conditions on relational priming with fractions. These findings are interpreted in terms of componential processing of fractions in a relational multiplication context that takes advantage of their inherent connections to a multiplicative schema for whole numbers. (shrink)

The present study examined whether a dissociation among formats for rational numbers can be obtained in tasks that require comparing a number to a non-symbolic quantity. In Experiment 1, college students saw a discrete or else continuous image followed by a rational number, and had to decide which was numerically larger. In Experiment 2, participants saw the same displays but had to make a judgment about the type of ratio represented by the number. The magnitude task was performed more quickly (...) using decimals, whereas the relation task was performed more accurately with fractions. The pattern observed for percentages was very similar to that for decimals. A dissociation between magnitude comparison and relational processing with rational numbers can be obtained when a symbolic number must be compared to a non-symbolic display. (shrink)

In our target article, we argued that there is a profound functional discontinuity between the cognitive abilities of modern humans and those of all other extant species. Unsurprisingly, our hypothesis elicited a wide range of responses from commentators. After responding to the commentaries, we conclude that our hypothesis lies closer to Darwin's views on the matter than to those of many of our contemporaries.

Advances in artificial intelligence have raised a basic question about human intelligence: Is human reasoning best emulated by applying task‐specific knowledge acquired from a wealth of prior experience, or is it based on the domain‐general manipulation and comparison of mental representations? We address this question for the case of visual analogical reasoning. Using realistic images of familiar three‐dimensional objects (cars and their parts), we systematically manipulated viewpoints, part relations, and entity properties in visual analogy problems. We compared human performance to (...) that of two recent deep learning models (Siamese Network and Relation Network) that were directly trained to solve these problems and to apply their task‐specific knowledge to analogical reasoning. We also developed a new model using part‐based comparison (PCM) by applying a domain‐general mapping procedure to learned representations of cars and their component parts. Across four‐term analogies (Experiment 1) and open‐ended analogies (Experiment 2), the domain‐general PCM model, but not the task‐specific deep learning models, generated performance similar in key aspects to that of human reasoners. These findings provide evidence that human‐like analogical reasoning is unlikely to be achieved by applying deep learning with big data to a specific type of analogy problem. Rather, humans do (and machines might) achieve analogical reasoning by learning representations that encode structural information useful for multiple tasks, coupled with efficient computation of relational similarity. (shrink)

Moral hypocrisy is typically viewed as an ethical accusation: Someone is applying different moral standards to essentially identical cases, dishonestly claiming that one action is acceptable while otherwise equivalent actions are not. We suggest that in some instances the apparent logical inconsistency stems from different evaluations of a weak argument, rather than dishonesty per se. Extending Corner, Hahn, and Oaksford's (2006) analysis of slippery slope arguments, we develop a Bayesian framework in which accusations of hypocrisy depend on inferences of shared (...) category membership between proposed actions and previous standards, based on prior probabilities that inform the strength of competing hypotheses. Across three experiments, we demonstrate that inferences of hypocrisy increase as perceptions of the likelihood of shared category membership between precedent cases and current cases increase, that these inferences follow established principles of category induction, and that the presence of self-serving motives increases inferences of hypocrisy independent of changes in the actions themselves. Taken together, these results demonstrate that Bayesian analyses of weak arguments may have implications for assessing moral reasoning. (shrink)

Reasoning requires making inferences based on information gleaned from a set of relations. The relational complexity of a problem increases with the number of relations that must be considered simultaneously to make a correct inference. Previous work (Viskontas, Morrison, Holyoak, Hummel, & Knowlton, 2004) has shown that older adults have difficulty integrating multiple relations during analogical reasoning, especially when required to inhibit irrelevant information. We report two experiments that examined the ability to integrate multiple relations in younger, middle-aged, and older (...) adults performing two other reasoning tasks. These tasks systematically varied relational complexity, and required either inductive reasoning (a version of the Raven's Matrices Task) or transitive inference. Our results show that as people age they have increasing difficulty in solving problems that require them to integrate multiple relations. This difficulty may stem from a decrease in working memory capacity. (shrink)

Solutions to word problems are moderated by the semantic alignment of real-world relations with mathematical operations. Categorical relations between entities are aligned with addition, whereas certain functional relations between entities are aligned with division. Similarly, discreteness vs. continuity of quantities is aligned with different formats for rational numbers. These alignments have been found both in textbooks and in the performance of college students in the USA and in South Korea. The current study examined evidence for alignments in Russia. Textbook analyses (...) revealed semantic alignments for arithmetic word problems, but not for rational numbers. Nonetheless, Russian college students showed semantic alignments both for arithmetic operations and for rational numbers. Since Russian students exhibit semantic alignments for rational numbers in the absence of exposure to examples in school, such alignments likely reflect intuitive understanding of mathematical representations of real-world situations. (shrink)

A key property of relational representations is their generativity: From partial descriptions of relations between entities, additional inferences can be drawn about other entities. A major theoretical challenge is to demonstrate how the capacity to make generative inferences could arise as a result of learning relations from non-relational inputs. In the present paper, we show that a bottom-up model of relation learning, initially developed to discriminate between positive and negative examples of comparative relations, can be extended to make generative inferences. (...) The model is able to make quasi-deductive transitive inferences and to qualitatively account for human responses to generative questions such as “What is an animal that is smaller than a dog?” These results provide evidence that relational models based on bottom-up learning mechanisms are capable of supporting generative inferences. (shrink)

The fundamental relations that underlie cognitive comparisons—“same” and “different”—can be defined at multiple levels of abstraction, which vary in relational complexity. We compared response times to decide whether or not two sequentially‐presented patterns, each composed of two pairs of colored squares, were the same at three levels of abstraction: perceptual, relational, and system (higher order relations). For both 150 ms and 5 s inter‐stimulus intervals (ISIs), both with and without a masking stimulus, decision time increased with level of abstraction. Sameness (...) at lower complexity levels contributed to decisions based on the higher levels. The pattern of comparison times across levelswas not predictable solely from encoding times. The results indicated that relations at multiple levels of complexity can be abstracted and compared in working memory, with higher complexity levels requiring more processing time. We simulated the impact of relational complexity on response time using Learning and Inference with Schemas and Analogies (LISA), a computational model of relational comparisons based on dynamic binding of elements into roles in a relational working memory. (shrink)

May's careful examination of empirical evidence makes a compelling case against the primacy of emotion in driving moral judgments. At the same time, emotion certainly is involved in moral judgments. We argue that emotion interacts with beliefs, values, and moral principles through a process of coherence-based reasoning (operating at least partially below the level of conscious awareness) in generating moral judgments and decisions.

Humans, including preschool children, exhibit role-based relational reasoning, of which analogical reasoning is a canonical example. The connectionist model proposed in the target article is only capable of conditional paired-associate learning.