Open AccessMathematical symbols as epistemic actions
Author(s) -
Helen De Cruz,
Johan De Smedt
Publication year - 2010
Publication title -
synthese
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.851
H-Index - 65
eISSN - 1573-0964
pISSN - 0039-7857
DOI - 10.1007/s11229-010-9837-9
Subject(s) - cognitive science , philosophy of science , cognition , philosophy of language , mathematical practice , numerical cognition , mathematical theory , mathematical psychology , epistemology , mathematical structure , language of mathematics , mathematical problem , mathematical model , computer science , metaphysics , psychology , mathematics , cognitive psychology , mathematics education , basic science , philosophy , physics , statistics , quantum mechanics , neuroscience
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.status: publishe
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