Synthese 190 (1):3-19 (2013)
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| 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.
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| 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
Religion Explained: The Evolutionary Origins of Religious Thought.Pascal Boyer - 2001 - Basic Books.
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Citations of this work BETA
Forms and Roles of Diagrams in Knot Theory.Silvia De Toffoli & Valeria Giardino - 2014 - Erkenntnis 79 (4):829-842.
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.
Extended Mathematical Cognition: External Representations with Non-Derived Content.Karina Vold & Dirk Schlimm - 2020 - Synthese 197 (9):3757-3777.
Philosophy of Mathematical Practice: A Primer for Mathematics Educators.Yacin Hamami & Rebecca Morris - forthcoming - ZDM Mathematics Education.
Existential Graphs as an Instrument of Logical Analysis: Part I. Alpha.Francesco Bellucci & Ahti-Veikko Pietarinen - 2016 - Review of Symbolic Logic 9 (2):209-237.
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