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Mathematics, Substance and Surmise

Views on the Meaning and Ontology of Mathematics

  • Book
  • © 2015

Overview

Editors:
  1. Ernest Davis

    1. Department of Computer Science, New York University, New York, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Philip J. Davis

    1. Department of Applied Mathematics, Brown University, Providence, USA

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    You can also search for this editor in PubMed   Google Scholar

  • Includes thought-provoking essays composed by renowned mathematicians, philosophers and historians of mathematics

  • Offers a modern and diverse viewpoint on mathematical ontology

  • Presents useful reading for students taking a course in philosophy of mathematics/science

  • Includes supplementary material: sn.pub/extras

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Table of contents (18 chapters)

  1. Front Matter

    Pages i-vi
    Download chapter PDF

  2. Introduction

    • Ernest Davis
    Pages 1-7

  3. Hardy, Littlewood and polymath

    • Ursula Martin, Alison Pease
    Pages 9-23

  4. Experimental computation as an ontological game changer: The impact of modern mathematical computation tools on the ontology of mathematics

    • David H. Bailey, Jonathan M. Borwein
    Pages 25-67

  5. Mathematical products

    • Philip J. Davis
    Pages 69-74

  6. How should robots think about space?

    • Ernest Davis
    Pages 75-99

  7. Mathematics and its applications

    • David Berlinski
    Pages 101-131

  8. Nominalism, the nonexistence of mathematical objects

    • Jody Azzouni
    Pages 133-145

  9. An Aristotelian approach to mathematical ontology

    • Donald Gillies
    Pages 147-176

  10. Let G be a group

    • Jesper Lützen
    Pages 177-192

  11. From the continuum to large cardinals

    • John Stillwell
    Pages 193-211

  12. Mathematics at infinity

    • Jeremy Gray
    Pages 213-234

  13. Mathematics and language

    • Jeremy Avigad
    Pages 235-255

  14. The linguistic status of mathematics

    • Micah T. Ross
    Pages 257-285

  15. Mathematics as multimodal semiosis

    • Kay L. O’Halloran
    Pages 287-303

  16. Problems in philosophy of mathematics: A view from cognitive science

    • Steven T. Piantadosi
    Pages 305-320

  17. Beliefs about the nature of numbers

    • Lance J. Rips
    Pages 321-345

  18. What kind of thing might number become?

    • Nathalie Sinclair
    Pages 347-363

  19. Enumerated entities in public policy and governance

    • Helen Verran
    Pages 365-379
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Keywords

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 O’Halloran

Alison Pease

Steven Piantadosi

Lance Rips

Micah T. Ross

Nathalie Sinclair

John Stillwell

Hellen Verran

Editors and Affiliations

  • Department of Computer Science, New York University, New York, USA

    Ernest Davis

  • Department of Applied Mathematics, Brown University, Providence, USA

    Philip J. Davis

Bibliographic Information

  • Book Title: Mathematics, Substance and Surmise

  • Book Subtitle: Views on the Meaning and Ontology of Mathematics

  • Editors: Ernest Davis, Philip J. Davis

  • DOI: https://doi.org/10.1007/978-3-319-21473-3

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2015

  • Hardcover ISBN: 978-3-319-21472-6Published: 28 November 2015

  • Softcover ISBN: 978-3-319-36530-5Published: 29 October 2016

  • eBook ISBN: 978-3-319-21473-3Published: 17 November 2015

  • Edition Number: 1

  • Number of Pages: VI, 379

  • Number of Illustrations: 12 b/w illustrations, 23 illustrations in colour

  • Topics: History of Mathematical Sciences, Philosophy of Science

  • Industry Sectors: Electronics

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