What is the Philosophy of Mathematics?

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


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.


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


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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

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