© 2015

Mathematics, Substance and Surmise

Views on the Meaning and Ontology of Mathematics

  • Ernest Davis
  • Philip J. Davis

Table of contents

  1. Front Matter
    Pages i-vi
  2. Ernest Davis
    Pages 1-7
  3. Ursula Martin, Alison Pease
    Pages 9-23
  4. Philip J. Davis
    Pages 69-74
  5. Ernest Davis
    Pages 75-99
  6. David Berlinski
    Pages 101-131
  7. Jesper Lützen
    Pages 177-192
  8. John Stillwell
    Pages 193-211
  9. Jeremy Gray
    Pages 213-234
  10. Jeremy Avigad
    Pages 235-255
  11. Micah T. Ross
    Pages 257-285
  12. Kay L. O’Halloran
    Pages 287-303
  13. Lance J. Rips
    Pages 321-345
  14. Nathalie Sinclair
    Pages 347-363

About this book


The seventeen thought-provoking and engaging essays in this collection present readers with a wide range of diverse perspectives on the ontology of mathematics. The essays address such questions as: What kind of things are mathematical objects? What kinds of assertions do mathematical statements make? How do people think and speak about mathematics?  How does society use mathematics? How have our answers to these questions changed over the last two millennia, and how might they change again in the future?   The authors include mathematicians, philosophers, computer scientists, cognitive psychologists, sociologists, educators, and mathematical historians; each brings their own expertise and insights to the discussion.

Contributors to this volume:

Jeremy Avigad

Jody Azzouni

David H. Bailey

David Berlinski

Jonathan M. Borwein

Ernest Davis

Philip J. Davis

Donald Gillies

Jeremy Gray

Jesper Lützen

Ursula Martin

Kay L. O’Halloran

Alison Pease

Steven T. Piantadosi

Lance J. Rips

Micah T. Ross

Nathalie Sinclair

John Stillwell

Helen Verran


mathematical objects mathematical ontology mathematical statements mathematical truths philosophy mathematics

Editors and affiliations

  • Ernest Davis
    • 1
  • Philip J. Davis
    • 2
  1. 1.Department of Computer ScienceNew York UniversityNew YorkUSA
  2. 2.Department of Applied MathematicsBrown UniversityProvidenceUSA

Bibliographic information