Numerical Cognition
Description
Over the past few decades, researchers have sought to address an array of fundamental issues regarding the human capacity for numerical cognition. Does the human mind contain innate representations of numbers and numerical properties? Do our perceptual states represent number? How do children acquire number concepts in the first few years of life? How does natural language encode number? What impact do cultural products, such as numeral systems and counting procedures, exert on human cognition? Such issues have been the subject of intensive research in several disciplines, including psychology, neuroscience, philosophy, linguistics, anthropology, and behavioral ecology. Yet the lines of communication between these fields have often been limited. Numerical Cognition: Debates & Disputes brings together thirty-two newly commissioned chapters by leading researchers from across these various fields. In doing so, it aims to foster interdisciplinary dialogue and to make insights from each of the contributing disciplines available to a broad academic audience.
More details
Persons
Eric Snyder, PhD, is Associate Professor of Philosophy at Ashoka University. Dr. Snyder specializes in the philosophy of language, logic, and the philosophy of mathematics, and has numerous publications of relevance to numerical cognition, especially concerning the semantics of number words.
Richard Samuels, PhD, is Professor and Chair in the Department of Philosophy at the Ohio State University. Dr. Samuels is a philosopher of mind and philosopher of science and has published extensively on issues concerning cognitive development, reasoning, modularity, computational models in cognitive science, and number cognition.
Content
Introduction.- The development of the perceptual number sense: current theories and debates.- Re-thinking the number sense: The perceptual interdependence account.- Numerosity and sensory processing in the human brain.- Cardinality, numerousness, and autoscaling: Revisiting the content and format of the approximate number system.- Number as a primary perceptual attribute.- Number, adaptation, and perception.- How do we perceive large numbers? A neurocomputational inquiry.- Why the approximate number system supports number concept nativism-even if there are no innate number concepts.- It's numbers all the way down.- Is nativism sufficient in the acquisition of number word meanings?.- Number concepts and the elastic mind.- Collections and numerical cognition.- Where does the concept set come from?.- Three contentious theoretical assumptions within number cognition research.- Acquiring numerical equality.- Going beyond four without counting: evidence from Mexican Sign Language.- Double counting.- Number as a window into developmental differences in the categorization and quantification of partial objects.- On the semantics of number (words) and degrees.- Numerical expressions and maximality: Semantic or pragmatic, lexical or compositional?.- Taxonomic uses of number words and their theoretical significance.- The role of syntax in numerical and mathematical processing.- Number development: The interplay between processes of ontogenesis, sociogenesis, and microgenesis.- An experimental history of number: Simulating the emergence of symbolic number.- On comparative studies of numeral systems.- Li(n)king numbers and space: Origins and limits.- Rethinking spatial-numerical associations origin: Comparative insights into biology, culture and competing theories.- Neuroscience of number percepts and concepts: the integration-divergence debate and its neural foundations.- Do U.S. children have any conceptual understanding of fraction arithmetic?.- Grasping numbers without our hands.- Debating numerical cognition abilities in non-human animals.