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

Helen De Cruz
Saint Louis University
Johan De Smedt
University of Ghent
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
Categories (categorize this paper)
DOI 10.1007/s11229-010-9837-9
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

 PhilArchive page | Other versions
Through your library

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.

View all 37 references / Add more references

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.

View all 18 citations / Add more citations

Similar books and articles

Syntax-Directed Discovery in Mathematics.David S. Henley - 1995 - Erkenntnis 43 (2):241 - 259.
Dictionary of Symbols of Mathematical Logic.Robert Feys (ed.) - 1969 - Amsterdam: North-Holland Pub. Co..
The Argument From Agreement and Mathematical Realism.Pieranna Garavaso - 1992 - Journal of Philosophical Research 17:173-187.
Mathematical Engineering and Mathematical Change.Jean‐Pierre Marquis - 1999 - International Studies in the Philosophy of Science 13 (3):245 – 259.
What Are Mathematical Coincidences ?M. Lange - 2010 - Mind 119 (474):307-340.
Logical Systems Containing Only a Finite Number of Symbols.Leon Henkin - 1967 - Montreal, Presses De l'Université De Montréal.


Added to PP index

Total views
1,599 ( #3,006 of 2,497,977 )

Recent downloads (6 months)
42 ( #20,347 of 2,497,977 )

How can I increase my downloads?


My notes