Pluralism in Mathematics: A New Position in Philosophy of Mathematics

  • Michèle Friend

Part of the Logic, Epistemology, and the Unity of Science book series (LEUS, volume 32)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Michèle Friend
    Pages 1-4
  3. Motivations for the Pluralist Position; Considerations from Familiar Positions

    1. Front Matter
      Pages 5-5
    2. Michèle Friend
      Pages 7-30
    3. Michèle Friend
      Pages 51-77
    4. Michèle Friend
      Pages 79-100
  4. Initial Presentation of Pluralism

    1. Front Matter
      Pages 101-101
    2. Michèle Friend
      Pages 103-120
    3. Michèle Friend
      Pages 121-133
    4. Michèle Friend
      Pages 135-149
    5. Michèle Friend
      Pages 151-172
  5. Transcendental Presentation of Pluralism

    1. Front Matter
      Pages 173-173
    2. Michèle Friend
      Pages 189-201
  6. Putting Pluralism to Work: Applications

    1. Front Matter
      Pages 203-203
    2. Michèle Friend
      Pages 205-217
    3. Michèle Friend
      Pages 239-256
    4. Michèle Friend
      Pages 257-258

About this book

Introduction

This book is about philosophy, mathematics and logic, giving a philosophical account of Pluralism which is a family of positions in the philosophy of mathematics. There are four parts to this book, beginning with a look at motivations for Pluralism by way of Realism, Maddy’s Naturalism, Shapiro’s Structuralism and Formalism.

In the second part of this book the author covers: the philosophical presentation of Pluralism; using a formal theory of logic metaphorically; rigour and proof for the Pluralist; and mathematical fixtures. In the third part the author goes on to focus on the transcendental presentation of Pluralism, and in part four looks at applications of Pluralism, such as a Pluralist approach to proof in mathematics and how Pluralism works in regard to together-inconsistent philosophies of mathematics. The book finishes with suggestions for further Pluralist enquiry.

In this work the author takes a deeply radical approach in developing a new position that will either convert readers, or act as a strong warning to treat the word ‘pluralism’ with care.  

Keywords

formalism and pluralism from formalism to pluralism from structuralism to pluralism metaphorical use of logic paradoxes of tolerance pluralist approaches in mathematics transcendental paradoxes

Authors and affiliations

  • Michèle Friend
    • 1
  1. 1.The George Washington UniversityWashingtonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-007-7058-4
  • Copyright Information Springer Science+Business Media Dordrecht 2014
  • Publisher Name Springer, Dordrecht
  • eBook Packages Humanities, Social Sciences and Law
  • Print ISBN 978-94-007-7057-7
  • Online ISBN 978-94-007-7058-4
  • Series Print ISSN 2214-9775
  • Series Online ISSN 2214-9783
  • About this book