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Connecting Humans to Equations

A Reinterpretation of the Philosophy of Mathematics

  • Ole Ravn
  • Ole Skovsmose

Part of the History of Mathematics Education book series (HME)

Table of contents

  1. Front Matter
    Pages i-xxiv
  2. Part I

    1. Front Matter
      Pages 1-3
    2. Ole Ravn, Ole Skovsmose
      Pages 5-20
    3. Ole Ravn, Ole Skovsmose
      Pages 21-35
    4. Ole Ravn, Ole Skovsmose
      Pages 37-49
  3. Part II

    1. Front Matter
      Pages 51-53
    2. Ole Ravn, Ole Skovsmose
      Pages 55-69
    3. Ole Ravn, Ole Skovsmose
      Pages 71-81
    4. Ole Ravn, Ole Skovsmose
      Pages 83-94
  4. Part III

    1. Front Matter
      Pages 95-96
    2. Ole Ravn, Ole Skovsmose
      Pages 97-106
    3. Ole Ravn, Ole Skovsmose
      Pages 107-119
    4. Ole Ravn, Ole Skovsmose
      Pages 121-132
  5. Part IV

    1. Front Matter
      Pages 133-135
    2. Ole Ravn, Ole Skovsmose
      Pages 137-149
    3. Ole Ravn, Ole Skovsmose
      Pages 151-162
    4. Ole Ravn, Ole Skovsmose
      Pages 163-173
  6. Back Matter
    Pages 175-188

About this book

Introduction

Connecting Humans to Equations: A Reinterpretation of the Philosophy of Mathematics presents some of the most important positions in the philosophy of mathematics, while adding new dimensions to this philosophy. Mathematics is an integral part of human and social life, meaning that a philosophy of mathematics must include several dimensions. This book describes these dimensions by the following four questions that structure the content of the book: Where is mathematics? How certain is mathematics? How social is mathematics? How good is mathematics?

These four questions refer to the ontological, epistemological, social, and ethical dimension of a philosophy of mathematics. While the ontological and epistemological dimensions have been explored in all classic studies in the philosophy of mathematics, the exploration of the book is unique in its social and ethical dimensions. It argues that the foundation of mathematics is deeply connected to human and social actions and that mathematics includes not just descriptive but also performative features. This human-centered and accessible interpretation of mathematics is relevant for students in mathematics, mathematics education, and any technical discipline and for anybody working with mathematics.


Keywords

Philosophy of mathematics history of mathematics Platonism Axiomatisation Mental relations Begriffsschrift Principia Mathematica Brouwer’s Intuitionism Geometric constructions

Authors and affiliations

  • Ole Ravn
    • 1
  • Ole Skovsmose
    • 2
  1. 1.Department of Learning and PhilosophyAalborg UniversityAalborgDenmark
  2. 2.Department of Learning and PhilosophyAalborg UniversityAalborgDenmark

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-01337-0
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Education
  • Print ISBN 978-3-030-01336-3
  • Online ISBN 978-3-030-01337-0
  • Series Print ISSN 2509-9736
  • Series Online ISSN 2509-9744
  • Buy this book on publisher's site