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What is the Philosophy of Mathematics?

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Connecting Humans to Equations

Part of the book series: History of Mathematics Education ((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 mathematics—as opposed to the traditional anti-human conceptions—even 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.

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Notes

  1. 1.

    Other examples of a two-dimensional organisation of a philosophy of mathematics are found in Jaquette (Ed.) (2002). Philosophy of Mathematics: An Anthology; and Bueno and Linnebo (Eds.) (2009). New Waves in the Philosophy of Mathematics.

  2. 2.

    Detailed studies of the concept of the ontological is in terms of mathematical fictionalism found in Bueno (2009); the relevance of a Fregian philosophy of mathematics is addressed in Cook (2009); the concept of truth is explored in great details in Koellner (2009); and a philosophy of applied mathematics is approached in Pincock (2009). These particular studies demonstrate the depth that can be reached within a 2-dimnetional philosophy of mathematics. This depth can also be experienced in George and Velleman’s (2002) work, which investigates, for instance, logicism, intuitionism and finitism, the latter of which represented an extreme version of intuitionism.

  3. 3.

    We have also received much inspiration from Davis and Hersh (1981, 1988).

  4. 4.

    See Almeide and Joseph (2009).

  5. 5.

    For a discussion of mathematics and culture , see for instance Bishop (1988) and D’Ambrosio (2006)

  6. 6.

    See Foucault (2000).

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Author information

Authors and Affiliations

  1. Department of Learning and Philosophy, Aalborg University, Aalborg, Denmark

    Ole Ravn & Ole Skovsmose

  2. Department of Mathematics Education, State University of São Paulo, (Universidade Estadual Paulista, Unesp), São Paulo, Brazil

    Ole Skovsmose

Authors
  1. Ole Ravn
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  2. Ole Skovsmose
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Ravn, O., Skovsmose, O. (2019). What is the Philosophy of Mathematics?. In: Connecting Humans to Equations . History of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-01337-0_12

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  • DOI: https://doi.org/10.1007/978-3-030-01337-0_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-01336-3

  • Online ISBN: 978-3-030-01337-0

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