History of Mathematics Subseries

The Essence of Numbers

Authors: Patras, Frédéric

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  • This is a unique book which systematically addresses the conceptual nature of numbers
  • Combines mathematics, philosophy and history as tools to account for the existence and essence of numbers
  • Draws on original analyses of key classical authors (Aristotle, Condillac, Frege, Husserl...)
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eBook $9.99
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  • ISBN 978-3-030-56700-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $17.99
price for USA in USD
About this book

This book considers the manifold possible approaches, past and present, to our understanding of the natural numbers. They are treated as epistemic objects: mathematical objects that have been subject to epistemological inquiry and attention throughout their history and whose conception has evolved accordingly. Although they are the simplest and most common mathematical objects, as this book reveals, they have a very complex nature whose study illuminates subtle features of the functioning of our thought.

Using jointly history, mathematics and philosophy to grasp the essence of numbers, the reader is led through their various interpretations, presenting the ways they have been involved in major theoretical projects from Thales onward. Some pertain primarily to philosophy (as in the works of Plato, Aristotle, Kant, Wittgenstein...), others to general mathematics (Euclid's Elements, Cartesian algebraic geometry, Cantorian infinities, set theory...).

Also serving as an introduction to the works and thought of major mathematicians and philosophers, from Plato and Aristotle to Cantor, Dedekind, Frege, Husserl and Weyl, this book will be of interest to a wide variety of readers, from scholars with a general interest in the philosophy or mathematics to philosophers and mathematicians themselves.

About the authors

Frédéric Patras, alumnus of the École Normale Supérieure and research director at CNRS, is a mathematician who has long been committed to philosophical studies. Also the author of a book on contemporary mathematical thinking (La pensée mathématique contemporaine), he has published and edited over a hundred works on various subjects. He is interested in what the philosophical tradition can bring to our current understanding of science and mathematics.

Table of contents (15 chapters)

Table of contents (15 chapters)
  • Introduction

    Pages 1-6

    Patras, Frédéric

  • The Lasting Influence of Pythagorism

    Pages 7-21

    Patras, Frédéric

  • The One and the Multiple

    Pages 23-33

    Patras, Frédéric

  • Mathematics and Reality

    Pages 35-44

    Patras, Frédéric

  • The Third Man Argument

    Pages 45-56

    Patras, Frédéric

Buy this book

eBook $9.99
price for USA in USD
  • ISBN 978-3-030-56700-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $17.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
The Essence of Numbers
Authors
Series Title
History of Mathematics Subseries
Series Volume
2278
Copyright
2020
Publisher
Springer International Publishing
Copyright Holder
The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
eBook ISBN
978-3-030-56700-2
DOI
10.1007/978-3-030-56700-2
Softcover ISBN
978-3-030-56699-9
Series ISSN
2193-1771
Edition Number
1
Number of Pages
XI, 176
Number of Illustrations
1 b/w illustrations
Additional Information
Translation from the French language edition: La possibilité des nombres by Fréderic Patras, © Presses Universitaires de France 2014. Published by Presses Universitaires de France. All Rights Reserved.
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