Mathematical symbols as epistemic actions
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.
KeywordsMathematical symbols Extended mind Symbolic cognition History of mathematics
Unable to display preview. Download preview PDF.
- Boyer P. (2001) Religion explained. The evolutionary origins of religious thought. Basic Books, New YorkGoogle Scholar
- Buzaglo M. (2002) The logic of concept expansion. Cambridge University Press, CambridgeGoogle Scholar
- De Morgan A. (1830) On the study and difficulties of mathematics. Paul Kegan, LondonGoogle Scholar
- Ernest P. (1998) Social constructivism as a philosophy of mathematics. State University of New York Press, AlbanyGoogle Scholar
- Joseph G. G. (2000) The crest of the peacock: Non-European roots of mathematics (2nd ed.). Princeton University Press, PrincetonGoogle Scholar
- Millikan R. G. (1998) A common structure for concepts of individuals, stuffs, and real kinds: More mama, more milk, and more mouse. Behavioral and Brain Sciences 21: 55–65Google Scholar
- Popper K. (1994) In search of a better world. Lectures and essays from thirty years. Routledge, LondonGoogle Scholar
- Schlimm D., Neth H. (2008) Modeling ancient and modern arithmetic practices: Addition and multiplication with Arabic and Roman numerals. In: Sloutsky V., Love B., McRae K. (eds) Proceedings of the 30th annual meeting of the Cognitive Science Society. Cognitive Science Society, AustinGoogle Scholar
- Sperber D. (1996) Explaining culture. A naturalistic approach. Blackwell, OxfordGoogle Scholar
- Tratman E. K. (1976) A late Upper Palaeolithic calculator (?), Gough’s cave, Cheddar, Somerset. Proceedings of the University of Bristol Spelæological Society 14: 123–129Google Scholar
- Whitehead A. N. (1911) An introduction to mathematics. Williams & Northgate, LondonGoogle Scholar