, Volume 190, Issue 1, pp 319
First online:
Mathematical symbols as epistemic actions
 Helen De CruzAffiliated withCentre for Logic and Analytical Philosophy, University of Leuven Email author
 , Johan De SmedtAffiliated withDepartment of Philosophy and Ethics, Ghent University
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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 casestudies 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 History of mathematics Title
 Mathematical symbols as epistemic actions
 Journal

Synthese
Volume 190, Issue 1 , pp 319
 Cover Date
 201301
 DOI
 10.1007/s1122901098379
 Print ISSN
 00397857
 Online ISSN
 15730964
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Mathematical symbols
 Extended mind
 Symbolic cognition
 History of mathematics
 Industry Sectors
 Authors

 Helen De Cruz ^{(1)}
 Johan De Smedt ^{(2)}
 Author Affiliations

 1. Centre for Logic and Analytical Philosophy, University of Leuven, Kardinaal Mercierplein 2, 3000, Leuven, Belgium
 2. Department of Philosophy and Ethics, Ghent University, Blandijnberg 2, 9000, Gent, Belgium