Synthese 190 (1):3-19 (2013)

Authors
Helen De Cruz
Saint Louis University
Johan De Smedt
University of Ghent
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 symbols  Extended mind  Symbolic cognition
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DOI 10.1007/s11229-010-9837-9
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References found in this work BETA

The Extended Mind.Andy Clark & David J. Chalmers - 1998 - Analysis 58 (1):7-19.
The Bounds of Cognition.Frederick Adams & Kenneth Aizawa - 2008 - Malden, MA, USA: Wiley-Blackwell.
Mathematical Truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.

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Citations of this work BETA

An Inquiry Into the Practice of Proving in Low-Dimensional Topology.Silvia De Toffoli & Valeria Giardino - 2015 - In Gabriele Lolli, Giorgio Venturi & Marco Panza (eds.), From Logic to Practice. Zurich, Switzerland: Springer International Publishing. pp. 315-336.

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