Synthese

, Volume 190, Issue 1, pp 3–19

Mathematical symbols as epistemic actions

Authors

    • Centre for Logic and Analytical PhilosophyUniversity of Leuven
  • Johan De Smedt
    • Department of Philosophy and EthicsGhent University
Article

DOI: 10.1007/s11229-010-9837-9

Cite this article as:
De Cruz, H. & De Smedt, J. Synthese (2013) 190: 3. doi:10.1007/s11229-010-9837-9

Abstract

Recent experimental evidence from developmental psychology and cognitive neuroscience indicates that humans are equipped with unlearned elementary mathematical skills. However, formal mathematics has properties that cannot be reduced to these elementary cognitive capacities. The question then arises how human beings cognitively deal with more advanced mathematical ideas. This paper draws on the extended mind thesis to suggest that mathematical symbols enable us to delegate some mathematical operations to the external environment. In this view, mathematical symbols are not only used to express mathematical concepts—they are constitutive of the mathematical concepts themselves. Mathematical symbols are epistemic actions, because they enable us to represent concepts that are literally unthinkable with our bare brains. Using case-studies from the history of mathematics and from educational psychology, we argue for an intimate relationship between mathematical symbols and mathematical cognition.

Keywords

Mathematical symbolsExtended mindSymbolic cognitionHistory of mathematics

Copyright information

© Springer Science+Business Media B.V. 2010