The Essence of Numbers

1. Auflage 2020
ISBN: 978-3-030-56699-9
Verlag: Springer International Publishing

Buch, Englisch, 176 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 295 g

Reihe: History of Mathematics Subseries

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.

Zielgruppe

Popular/general

Autoren/Hrsg.

Patras, Frédéric

Fachgebiete

• Geisteswissenschaften Philosophie Moderne Philosophische Disziplinen Phänomenologie
• Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik
• Geisteswissenschaften Geschichtswissenschaft Geschichtliche Themen Kultur- und Ideengeschichte
• Mathematik | Informatik Mathematik Mathematik Allgemein Geschichte der Mathematik
• Geisteswissenschaften Philosophie Wissenschaftstheorie, Wissenschaftsphilosophie
• Geisteswissenschaften Philosophie Philosophie: Allgemeines, Methoden
• Geisteswissenschaften Geschichtswissenschaft Geschichtliche Themen Wissenschafts- und Universitätsgeschichte
• Geisteswissenschaften Philosophie Philosophie der Mathematik, Philosophie der Physik

Inhaltsverzeichnis

- Introduction. - The Lasting Influence of Pythagorism. - The One and the Multiple. - Mathematics and Reality. - The Third Man Argument. - Numbers and Magnitudes. - Generalized Numbers I. - Generalized Numbers II. - Cantor and Set Theory. - Frege’s Logicism. - Set Theory in Frege. - Axioms and Formalisms. - The Brain and Cognitive Processes. - Phenomenology of Numbers. - Universal Phenomena, Algebra, Categories.

Über Autor(innen)

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.