Analogical Truth-Conditions for Metaphors

It has often been said that metaphors are based on analogies, but the nature of this relation has never been made precise. This article rigorously and formally specifies two semantic relations that do obtain between some metaphors and analogies. We argue that analogies often provide conditions of meaningfulness and truth for metaphors. An analogy is treated as an isomorphism from a source to topic domain. Metaphors are thought of as surface structures. Formal analogical conditions of meaningfulness and truth are fully and rigorously worked out for several grammatical classes of metaphors. By providing analogical meaningfulness and truth conditions for metaphors, this article shows that truth-conditional semantics can be extended to metaphors

Children’s spontaneous comparisons from 26 to 58 months predict performance in verbal and non-verbal analogy tests in 6th grade

Comparison supports the development of children’s analogical reasoning. The evidence for this claim comes from laboratory studies. We describe spontaneous comparisons produced by 24 typically developing children from 26 to 58 months. Children tend to express similarity before expressing difference. They compare objects from the same category before objects from different categories, make global comparisons before specific comparisons, and specify perceptual features of similarity/difference before non-perceptual features. We then investigate how a theoretically interesting subset of children’s comparisons – those expressing a specific feature of similarity or difference – relates to analogical reasoning as measured by verbal and non-verbal tests in 6th grade. The number of specific comparisons children produce before 58 months predicts their scores on both tests, controlling for vocabulary at 54 months. The results provide naturalistic support for experimental findings on comparison development, and demonstrate a strong relationship between children’s early comparisons and their later analogical reasoning

When almost is not even close: Remarks on the approximability of HDTP

A growing number of researchers in Cognitive Science advocate the thesis that human cognitive capacities are constrained by computational tractability. If right, this thesis also can be expected to have far-reaching consequences for work in Artificial General Intelligence: Models and systems considered as basis for the development of general cognitive architectures with human-like performance would also have to comply with tractability constraints, making in-depth complexity theoretic analysis a necessary and important part of the standard research and development cycle already from a rather early stage. In this paper we present an application case study for such an analysis based on results from a parametrized complexity and approximation theoretic analysis of the Heuristic Driven Theory Projection (HDTP) analogy-making framework

Comparison and Mapping Facilitate Relation Discovery and Predication

Relational concepts play a central role in human perception and cognition, but little is known about how they are acquired. For example, how do we come to understand that physical force is a higher-order multiplicative relation between mass and acceleration, or that two circles are the same-shape in the same way that two squares are? A recent model of relational learning, DORA (Discovery of Relations by Analogy; Doumas, Hummel & Sandhofer, 2008), predicts that comparison and analogical mapping play a central role in the discovery and predication of novel higher-order relations. We report two experiments testing and confirming this prediction

Metaphors We Think With: The Role of Metaphor in Reasoning

The way we talk about complex and abstract ideas is suffused with metaphor. In five experiments, we explore how these metaphors influence the way that we reason about complex issues and forage for further information about them. We find that even the subtlest instantiation of a metaphor (via a single word) can have a powerful influence over how people attempt to solve social problems like crime and how they gather information to make “well-informed” decisions. Interestingly, we find that the influence of the metaphorical framing effect is covert: people do not recognize metaphors as influential in their decisions; instead they point to more “substantive” (often numerical) information as the motivation for their problem-solving decision. Metaphors in language appear to instantiate frame-consistent knowledge structures and invite structurally consistent inferences. Far from being mere rhetorical flourishes, metaphors have profound influences on how we conceptualize and act with respect to important societal issues. We find that exposure to even a single metaphor can induce substantial differences in opinion about how to solve social problems: differences that are larger, for example, than pre-existing differences in opinion between Democrats and Republicans

Students’ analogical reasoning in novel situations: theory-like misconceptions or p-prims?

Over the past 50 years there has been much research in the area of students' misconceptions. Whilst this research has been useful in helping to inform the design of instructional approaches and curriculum development it has not provided much insight into how students reason when presented with a novel situation and, in particular, the knowledge they draw upon in an attempt to make predictions about that novel situation. This article reports on a study of Greek students, aged from 10 to 17 years old, who were asked to make predictions in novel situations and to then provide, without being told whether their predictions were correct or incorrect, explanations about their predictions. Indeed, their explanations in such novel situations have the potential to reveal how their ideas, as articulated as predictions, are formed as well as the sources they draw upon to make those predictions. We also consider in this article the extent to which student ideas can be seen either as theory-like misconceptions or, alternatively, as situated acts of construction involving the activation of fragmented pieces of knowledge referred to as phenomenological primitives (p-prims). Our findings suggest that in most cases students' reasoning in novel situations can be better understood in terms of their use of p-prims and that teaching might be made more effective if teachers were more aware of the p-prims that students were likely to be using when presented with new situations in physics