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2 results

Introducing the Philosophy of Mathematical Practice

Introducing the Philosophy of Mathematical Practice
  • Jessica Carter
  • Published online:
    27 November 2024
    Print publication:
    02 January 2025
  • This Element introduces a young field, the 'philosophy of mathematical practice'. We first offer a general characterisation of the approach to the philosophy of mathematics that takes mathematical practice seriously and contrast it with 'mathematical philosophy'. The latter is traced back to Bertrand Russell and the orientation referred to as 'scientific philosophy' that was active between 1850 and 1930. To give a better sense of the field, the Element further contains two examples of topics studied, that of mathematical structuralism and visual thinking in mathematics. These are in part presented from a methodological point of view, focussing on mathematics as an activity and questions related to how mathematics develops. In addition, the Element contains several examples from mathematics, both historical and contemporary , to illustrate and support the philosophical points.

  • 2 - Metaphysics of Mathematics

  • Leon Horsten, University of Bristol
  • Book:
    The Metaphysics and Mathematics of Arbitrary Objects
    Published online:
    24 May 2019
    Print publication:
    13 June 2019, pp 13-37

  • Summary

    This chapter deals with methodological questions. The methodological approach that is advocated in this chapter leaves little room for realism debates in philosophy. In particular, from the next chapter onwards, questions of realism in metaphysics and in philosophy of mathematics are left mostly aside. Instead, I will be doing what Kit Fine calls \emph{naive metaphysics}.