Advertisement

What is the Philosophy of Mathematics?

  • Ole Ravn
  • Ole Skovsmose
Chapter
Part of the History of Mathematics Education book series (HME)

Abstract

This chapter addresses different conceptions of the philosophy of mathematics. Classic positions become characterised as two-dimensional by concentrating on ontological and epistemological issues. As an alternative, a four-dimensional philosophy of mathematics become presented by expanding the philosophy to include a social and a ethical dimension as well.

The book has elaborated upon a four-dimensional philosophy of mathematics, but it does not make any claim about the adequate number of dimensions. Its main point has been to move beyond any two-dimensional philosophy, and in this move to establish human beings as having an all-important role in mathematics. By having opened a space for a humanised conception of mathematicsas opposed to the traditional anti-human conceptionseven more dimensions may emerge, as for instance an aesthetic and a political dimension. This leads to the more general question: What could it mean to move beyond the borders set by the Western tradition in the philosophy of mathematics? In fact, one comes to acknowledge the possibility that a philosophy of mathematics may stretch beyond the borders set by philosophy itself.

Keywords

Beyond the philosophy of mathematics Beyond the Western philosophy of mathematics Dimensions of philosophy of mathematics Epistemology Ontology 

References

  1. Almeida, D. F., & Joseph, G. G. (2009). Kerala mathematics and its possible transmission to Europe. In P. Ernest, B. Greer, & B. Sriraman (Eds.), Critical issues in mathematics education (pp. 171–188). Charlotte, NC: Information Age Publishing.Google Scholar
  2. Bernacerraf, P., & Putnam, H. (Eds.). (1964). Philosophy of mathematics. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
  3. Bishop, A. (1988). Mathematical enculturation. Dordrecht, The Netherlands: Kluwer Academic Publishers.CrossRefGoogle Scholar
  4. Bueno, O., & Linnebo, Ø. (Eds.). (2009). New waves in the philosophy of mathematics. Basingstoke, Hampshire, UK: Palgrave Macmillan.Google Scholar
  5. Cook, R. T. (2009). New waves on an old beach: Fregian philosophy of mathematics today. In O. Bueno & Ø. Linnebo (Eds.), New waves in the philosophy of mathematics (pp. 13–14). Basingstoke, Hampshire, UK: Palgrave Macmillan.CrossRefGoogle Scholar
  6. D’Ambrosio, U. (2006). Ethnomathematics: Link between traditions and modernity. Rotterdam, The Netherlands: Sense Publishers.Google Scholar
  7. Davis, P. J., & Hersh, R. (1981). The mathematical experience. Boston, MA: Birkhäuser.Google Scholar
  8. Davis, P. J., & Hersh, R. (1988). Descartes dream: The world according to mathematics. Harmondsworth, UK: Penguin Books.Google Scholar
  9. Ernest, P. (1998). Social constructivism as a philosophy of mathematics. Albany, NY: State University of New York Press..Google Scholar
  10. Foucault, M. (2000). In J. D. Faubion (Ed.), Power. New York, NY: The New Press.Google Scholar
  11. George, A., & Velleman, D. J. (2002). Philosophies of mathematics. Malden, MA: Blackwell Publishers.Google Scholar
  12. Grabiner, J. V. (1986). Is mathematical truth time-dependent? In T. Tymoczko (Ed.), New directions in the philosophy of mathematics (pp. 201–213). Boston, MA: Birkhäuser.Google Scholar
  13. Hersh, R. (1998). What is mathematics, really? London, UK: Vintage.Google Scholar
  14. Jaquette, D. (Ed.). (2002). Philosophy of mathematics: An anthology. Malden, MA: Blackwell Publishers.Google Scholar
  15. Joseph, G. G. (2000). The crest of the peacock: The non-European roots of mathematics. Princeton, NJ: Princeton University Press.Google Scholar
  16. Koellner, P. (2009). Truth in mathematics: The question of pluralism. In O. Bueno & Ø. Linnebo (Eds.), New waves in the philosophy of mathematics (pp. 80–116). Basingstoke, Hampshire, UK: Palgrave Macmillan.CrossRefGoogle Scholar
  17. Körner, S. (1968). The philosophy of mathematics. London, UK: Hutchinson University Library.Google Scholar
  18. Pincock, C. (2009). Towards a philosophy of applied mathematics. In O. Bueno & Ø. Linnebo (Eds.), New waves in the philosophy of mathematics (pp. 173–194). Basingstoke, Hampshire, UK: Palgrave Macmillan.CrossRefGoogle Scholar
  19. Russell, B. (1978). Autobiography. London, UK: Unwin Paperbacks.Google Scholar
  20. Said, E. (1979). Orientalism. New York, NY: Vintage Books.Google Scholar
  21. Shapiro, S. (2000). Thinking about mathematics: The philosophy of mathematics. Oxford, UK: Oxford University Press.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ole Ravn
    • 1
  • Ole Skovsmose
    • 1
    • 2
  1. 1.Department of Learning and PhilosophyAalborg UniversityAalborgDenmark
  2. 2.Department of Mathematics EducationState University of São Paulo, (Universidade Estadual Paulista, Unesp)São PauloBrazil

Personalised recommendations