Synthese 190 (1):3-19 (2013)
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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Citations of this work BETA
Evolutionary Approaches to Epistemic Justification.Helen de Cruz, Maarten Boudry, Johan de Smedt & Stefaan Blancke - 2011 - Dialectica 65 (4):517-535.
Idealization and External Symbolic Storage: The Epistemic and Technical Dimensions of Theoretic Cognition.Peter Woelert - 2012 - Phenomenology and the Cognitive Sciences 11 (3):335-366.
Are Evolutionary Debunking Arguments Really Self-Defeating?Fabio Sterpetti - 2015 - Philosophia 43 (3):877-889.
Script and Symbolic Writing in Mathematics and Natural Philosophy.Maarten Van Dyck & Albrecht Heeffer - 2014 - Foundations of Science 19 (1):1-10.
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