The Essence of Numbers

The Essence of Numbers
  • eBook:
    The Essence of Numbers
  • Author:
    Frédéric Patras
  • Edition:
    1st ed. 2020 Edition
  • Categories:
  • Data:
    November 7, 2020
  • ISBN:
  • ISBN-13:
  • Language:
  • Pages:
    187 pages
  • Format:
    PDF, ePUB

Book Description
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.


1. Introduction
2. The Lasting Influence of Pythagorism
3. The One and the Multiple
4. Mathematics and Reality
5. The Third Man Argument
6. Numbers and Magnitudes
7. Generalized Numbers I
8. Generalized Numbers II
9. Cantor and Set Theory
10. Frege’s Logicism
11. Set Theory in Frege
12. Axioms and Formalisms
13. The Brain and Cognitive Processes
14. Phenomenology of Numbers
15. Universal Phenomena, Algebra, Categories

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