In acquiring number words, children exhibit a qualitative leap in which they transition from understanding a few number words, to possessing a rich system of interrelated numerical concepts. We present a computational framework for understanding this inductive leap as the consequence of statistical inference over a sufficiently powerful…

Concept learning is challenging in part because the meanings of many concepts depend on their relationships to other concepts. Learning these concepts in isolation can be difficult, but we present a model that discovers entire systems of related concepts. These systems can be viewed as simple theories that specify the concepts that exist in a…

According to one theory about how children learn the meaning of the words for the positive integers, they first learn that "one," "two," and "three" stand for appropriately sized sets. They then conclude by inductive inference that the next numeral in the count sequence denotes the size of sets containing one more object than the size denoted by…

Theories of number concepts often suppose that the natural numbers are acquired as children learn to count and as they draw an induction based on their interpretation of the first few count words. In a bold critique of this general approach, Rips, Asmuth, Bloomfield [Rips, L., Asmuth, J. & Bloomfield, A. (2006). Giving the boot to the bootstrap:…

The ability to automatically and implicitly detect complex and noisy regularities in the environment is a fundamental aspect of human cognition. Despite considerable interest in implicit processes, few researchers have conceptualized implicit learning as an ability with meaningful individual differences. Instead, various researchers (e.g., Reber,…

Children aged 6 to l7 were taught novel class inclusion hierarchies, analogous to the relation among oaks, pines, and trees. The results indicated that the part-whole structure of collections is simpler to establish and maintain than the structure of inclusion. (Author/RL)

Previous research (e.g. "Cognition" 64 (1997) 73) suggests that the privileged level for inductive inference in a folk biological conceptual hierarchy does not correspond to the ''basic'' level (i.e. the level at which concepts are both informative and distinct). To further explore inductive inference within conceptual hierarchies, we examine…

Conservation judgments are based on a combination of logical necessity and empirical belief. Results of two experiments support the view that the logical aspect of conservation is developmentally stable, while the empirical aspect varies widely across problems and individuals because of its dependence on relevant experience. (Author/RD)