Foundational Theories of Classical and Constructive Mathematics

  • Giovanni Sommaruga

Part of the The Western Ontario Series in Philosophy of Science book series (WONS, volume 76)

Table of contents

  1. Front Matter
    Pages i-lxi
  2. Senses of ‘Foundations of Mathematics’

    1. Front Matter
      Pages 51-51
    2. Geoffrey Hellman*
      Pages 53-69
    3. Penelope Maddy
      Pages 85-96
    4. Stewart Shapiro
      Pages 97-110
  3. Foundations of Classical Mathematics

    1. Front Matter
      Pages 111-111
    2. Steve Awodey
      Pages 113-125
    3. Colin McLarty
      Pages 145-154
  4. Between Foundations of Classical and Foundations of Constructive Mathematics

    1. Front Matter
      Pages 155-155
    2. Joachim Lambek, Philip J. Scott
      Pages 171-186
  5. Foundations of Constructive Mathematics

    1. Front Matter
      Pages 187-187
    2. Charles McCarty
      Pages 209-225
    3. Paul Taylor
      Pages 265-310
    4. Giovanni Sommaruga, John Bell
      Pages 311-314

About this book

Introduction

The book “Foundational Theories of Classical and Constructive Mathematics” is a book on the classical topic of foundations of mathematics. Its originality resides mainly in its treating at the same time foundations of classical and foundations of constructive mathematics. This confrontation of two kinds of foundations contributes to answering questions such as: Are foundations/foundational theories of classical mathematics of a different nature compared to those of constructive mathematics? Do they play the same role for the resp. mathematics? Are there connections between the two kinds of foundations? Etc. The confrontation and comparison is often implicit and sometimes explicit. Its great advantage is to extend the traditional discussion of foundations of mathematics and to render it at the same time more subtle and more differentiated.
Another important aspect of the book is that some of its contributions are of a more philosophical, others of a more technical nature. This double face is emphasized, since foundations of mathematics is an eminent topic in the philosophy of mathematics: hence both sides of this discipline ought to be and are being paid due to.

Keywords

classical mathematics constructive mathematics foundations of mathematics philosophy of mathematics

Editors and affiliations

  • Giovanni Sommaruga
    • 1
  1. 1.Dépt. d'InformatiqueUniversité de FribourgFribourgSwitzerland

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-007-0431-2
  • Copyright Information Springer Science+Business Media B.V. 2011
  • Publisher Name Springer, Dordrecht
  • eBook Packages Humanities, Social Sciences and Law
  • Print ISBN 978-94-007-0430-5
  • Online ISBN 978-94-007-0431-2
  • Series Print ISSN 1566-659X
  • About this book
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