Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-27T22:03:54.788Z Has data issue: false hasContentIssue false
  • English
  • Français

Proto-numerosities and concepts of number: Biologically plausible and culturally mediated top-down mathematical schemas

Published online by Cambridge University Press:  11 December 2008

Rafael E. Núñez
Rafael E. Núñez
Affiliation:
Department of Cognitive Science, University of California, San Diego, La Jolla, CA 92093-0515rnunez@ucsd.eduhttp://www.cogsci.ucsd.edu/~nunez/web/index.html
Get access Rights & Permissions [Opens in a new window]

Abstract

Early quantitative skills cannot be directly extended to provide the richness, precision, and sophistication of the concept of natural number. These skills must interact with top-down mathematical schemas, which can be explained by bodily grounded everyday mechanisms for abstraction and imagination (e.g., conceptual metaphor, blending) that are both biologically plausible and culturally shaped (established beyond the child's mind).

Type
Open Peer Commentary
Information
Behavioral and Brain Sciences , Volume 31 , Issue 6 , December 2008 , pp. 665 - 666
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Butterworth, B. (1997) What counts: How every brain is hardwired for math. The Free Press.Google Scholar
Dehaene, S. (2002) Single-neuron arithmetic. Science 297:1652–53.CrossRefGoogle ScholarPubMed
Fauconnier, G. & Turner, M. (2002) The way we think: Conceptual blending and the mind's hidden complexities. Basic Books.
Gallese, V. & Lakoff, G. (2005) The brain's concepts: The role of the sensory-motor system in conceptual knowledge. Cognitive Neuropsychology 22:455–79.Google Scholar
Gallistel, C. R., Gelman, R. & Cordes, S. (2006) The cultural and evolutionary history of the real numbers. In: Evolution and culture, ed. Levinson, S. C. & Jaisson, P., pp. 247–74. MIT Press.Google Scholar
Lakoff, G. (1993) The contemporary theory of metaphor. In: Metaphor and thought, 2nd edition, ed. Ortony, A., pp. 202–51. Cambridge University Press.Google Scholar
Lakoff, G. & Núñez, R. E. (2000) Where mathematics comes from: How the embodied mind brings mathematics into being. Basic Books.Google Scholar
Núñez, R. E. (2006) Do real numbers really move? Language, thought, and gesture: The embodied cognitive foundations of mathematics. In: 18 unconventional essays on the nature of mathematics, ed. Hersh, R., pp. 160–81. Springer.Google Scholar
Núñez, R. E. (2008) Mathematics, the ultimate challenge to embodiment: Truth and the grounding of axiomatic systems. In: Handbook of cognitive science: An embodied approach, ed. Calvo, P. & Gomila, T., pp. 333–53. Elsevier.CrossRefGoogle Scholar
Núñez, R. E. (in press) Enacting infinity: Bringing transfinite cardinals into being. In: Enaction: Towards a new paradigm in cognitive science, ed. Stewart, J., Gapenne, O. & Di Paolo, E.. MIT Press.Google Scholar
Núñez, R. E., Huang, R-S. & Sereno, M. (2007) Neural basis of metaphorical abstraction: An fMRI study of ego-reference-point spatial construals of time. In: 2007 Annual Meeting Cognitive Neuroscience Society, ed. Cognitive Neuroscience Society, pp. 284–85. MIT Press.Google Scholar
Núñez, R. E. & Sweetser, E. (2006) With the future behind them: Convergent evidence from Aymara language and gesture in the crosslinguistic comparison of spatial construals of time. Cognitive Science 30:401–50.CrossRefGoogle ScholarPubMed