Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T04:43:48.372Z Has data issue: false hasContentIssue false
  • English
  • Français

Is Mathematical Competence Innate?

Published online by Cambridge University Press:  01 April 2022

Robert Schwartz
Robert Schwartz*
Affiliation:
Department of Philosophy University of Wisconsin—Milwaukee
Get access Rights & Permissions [Opens in a new window]

Abstract

Despite a vast philosophical literature on the epistemology of mathematics and much speculation about how, in principle, knowledge of this domain is possible, little attention has been paid to the psychological findings and theories concerning the acquisition, comprehension and use of mathematical knowledge. This contrasts sharply with recent philosophical work on language where comparable issues and problems arise. One topic that is the center of debate in the study of mathematical cognition is the question of innateness. This paper critically examines the controversy.

Type
Research Article
Information
Philosophy of Science , Volume 62 , Issue 2 , June 1995 , pp. 227 - 240
Copyright
Copyright © Philosophy of Science Association 1995

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.)

Footnotes

†

An earlier version of this paper was presented at a Society for Philosophy and Psychology symposium. Karen Wynn was the other speaker and Robert Matthews provided thoughtful comments. I hope it is clear that my aim here is not to support “anti-nativist,” “empiricist” doctrines, but to downplay the significance of such labels by bringing into focus what the genuine issues are. A further goal of this essay is to provide a basis for comparing and contrasting arguments and claims in mathematical cognition with those found in language studies. Space limitations, however, preclude much discussion of the likenesses and differences found.

My work was supported by an N.E.H. Fellowship.

‡

Send reprint requests to the author, Department of Philosophy, University of Wisconsin—Milwaukee, P.O. Box 413, Milwaukee, WI 53201.

References

Chomsky, N. (1980), “Rules and Representations”, Behavioral and Brain Sciences 3: 1–61.10.1017/S0140525X00001515CrossRefGoogle Scholar
Chomsky, N. (1982), The Generative Enterprise. Dordrecht: Foris Publications.Google Scholar
Chomsky, N. (1984), Modular Approaches to the Study of Mind. San Diego: San Diego State University Press.Google Scholar
Chomsky, N. (1988), Language and Problems of Knowledge. Cambridge, MA: MIT Press.Google Scholar
Davis, H., and Perusse, R. (1988), “Numerical Competence in Animals”, Behavioral and Brain Sciences 11: 561–615.10.1017/S0140525X00053437CrossRefGoogle Scholar
Fodor, J. (1983), The Modularity of Mind. Cambridge, MA: MIT Press.10.7551/mitpress/4737.001.0001CrossRefGoogle Scholar
Fuson, K. (1988), Children's Counting and Concepts of Number. New York: Springer-Verlag.10.1007/978-1-4612-3754-9CrossRefGoogle Scholar
Gallistel, C. R. (1990), The Organization of Learning. Cambridge, MA: MIT Press.Google Scholar
Gallistel, C. R., and Gelman, R. (1990), “The What and How of Counting”, Cognition 34: 197–199.10.1016/0010-0277(90)90043-JCrossRefGoogle ScholarPubMed
Gallistel, C. R., and Gelman, R. (1991), “Subsitizing: The Preverbal Counting Process”, in Kessen, W., Ortony, A. and Craik, F. (eds.), Memories, Thoughts and Emotions. Hillsdale: Lawrence Erlbaum, 65–81.Google Scholar
Galloway, D. (1992), “Wynn on Mathematical Empiricism”, Mind and Language 7: 333–358.10.1111/j.1468-0017.1992.tb00307.xCrossRefGoogle Scholar
Gelman, R., and Gallistel, C. R. (1978), The Child's Understanding of Number. Cambridge, MA: Harvard University Press.Google Scholar
Gelman, R., and Meck, E. (1986) “The Notion of Principle”, in Hiebert, J. (ed.), Conceptual and Procedural Knowledge. Hillsdale: Lawrence Erlbaum, 29–57.Google Scholar
Keil, F. (1990), “Constraints on Constraints”, Cognitive Science 14: 135–168.10.1207/s15516709cog1401_7CrossRefGoogle Scholar
Piaget, J. (1952), The Child's Conception of Number. New York: Norton.Google Scholar
Premack, D. (1976), Intelligence in Ape and Man. New York: John Wiley.Google Scholar
Quine, W. V. (1974), The Roots of Reference. LaSalle: Open Court.Google Scholar
Rosenthal, D. (1980), “Comments”, Behavioral and Brain Sciences 3: 32–34.10.1017/S0140525X00001692CrossRefGoogle Scholar
Shipley, E., and Shepperson, B. (1990), “Countable Entities”, Cognition 34: 109–136.10.1016/0010-0277(90)90041-HCrossRefGoogle ScholarPubMed
Starkey, P., and Cooper, R. (1980), “Perception of Number by Human Infants”, Science 210: 1033–1035.10.1126/science.7434014CrossRefGoogle ScholarPubMed
Starkey, P., Spelke, E., and Gelman, R. (1983), “Detection of Intermodal Numerical Correspondence by Human Infants”, Science 222: 179–181.10.1126/science.6623069CrossRefGoogle Scholar
Starkey, P., Spelke, E., and Gelman, R. (1990), “Numerical Abstraction by Human Infants”, Cognition 36: 97–127.10.1016/0010-0277(90)90001-ZCrossRefGoogle ScholarPubMed
Sugarman, S. (1983), Children's Early Thought. Cambridge: Cambridge University Press.Google Scholar
Wynn, K. (1990), “Children's Understanding of Counting”, Cognition 36: 155–193.10.1016/0010-0277(90)90003-3CrossRefGoogle ScholarPubMed
Wynn, K. (1992a), “Addition and Subtraction by Human Infants”, Nature 358, 749–750.10.1038/358749a0CrossRefGoogle Scholar
Wynn, K. (1992b), “Evidence Against Empirical Accounts of the Origins of Numerical Knowledge”, Mind and Language 7: 315–332.10.1111/j.1468-0017.1992.tb00306.xCrossRefGoogle Scholar
Wynn, K. (1992c), “Issues Concerning a Nativist Theory of Numerical Knowledge”, Mind and Language 7: 367–381.10.1111/j.1468-0017.1992.tb00310.xCrossRefGoogle Scholar