Overview
- 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...)
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2278)
Part of the book sub series: History of Mathematics Subseries (HISTORYMS)
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Table of contents (15 chapters)
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Front Matter
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Back Matter
Keywords
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.
Reviews
Authors and Affiliations
About the author
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.
Bibliographic Information
Book Title: The Essence of Numbers
Authors: Frédéric Patras
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-030-56700-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
Softcover ISBN: 978-3-030-56699-9Published: 07 October 2020
eBook ISBN: 978-3-030-56700-2Published: 06 October 2020
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
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.
Topics: History of Mathematical Sciences, Philosophy of Mathematics, Philosophy of Science, Cultural History, Philosophy, general, Phenomenology