, Volume 190, Issue 1, pp 3–19

Mathematical symbols as epistemic actions


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


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.


Mathematical symbols Extended mind Symbolic cognition History of mathematics 

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Centre for Logic and Analytical PhilosophyUniversity of LeuvenLeuvenBelgium
  2. 2.Department of Philosophy and EthicsGhent UniversityGentBelgium