Mathematical symbols as epistemic actions

Synthese 190 (1):3-19 (2013)
Download Edit this record How to cite View on PhilPapers
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.
PhilPapers/Archive ID
Revision history
Archival date: 2012-12-10
View upload history
References found in this work BETA
The Extended Mind.Clark, Andy & Chalmers, David J.
Core Systems of Number.Dehaene, Stanislas; Spelke, Elizabeth & Feigenson, Lisa
The Bounds of Cognition.Adams, Fred & Aizawa, Ken

View all 34 references / Add more references

Citations of this work BETA
Evolutionary Approaches to Epistemic Cruz, Helen; Boudry, Maarten; de Smedt, Johan & Blancke, Stefaan
Forms and Roles of Diagrams in Knot Theory.De Toffoli, Silvia & Giardino, Valeria

View all 13 citations / Add more citations

Added to PP index

Total views
1,079 ( #1,908 of 43,009 )

Recent downloads (6 months)
111 ( #4,126 of 43,009 )

How can I increase my downloads?

Downloads since first upload
This graph includes both downloads from PhilArchive and clicks to external links.