Philosophy of Mathematics and Natural Science

by Hermann Weyl, Frank Wilczek (Introduction)

Overview

When mathematician Hermann Weyl decided to write a book on philosophy, he faced what he referred to as "conflicts of conscience"—the objective nature of science, he felt, did not mesh easily with the incredulous, uncertain nature of philosophy. Yet the two disciplines were already intertwined. In Philosophy of Mathematics and Natural Science, Weyl examines how advances in philosophy were led by scientific discoveries—the more humankind understood about the physical world, the more curious we became. The book is divided into two parts, one on mathematics and the other on the physical sciences. Drawing on work by Descartes, Galileo, Hume, Kant, Leibniz, and Newton, Weyl provides readers with a guide to understanding science through the lens of philosophy. This is a book that no one but Weyl could have written—and, indeed, no one has written anything quite like it since.

Product Details

ISBN-13:	9780691141206
Publisher:	Princeton University Press
Publication date:	05/17/2009
Edition description:	With a New introduction by Frank Wilczek
Pages:	336
Product dimensions:	5.90(w) x 8.90(h) x 0.90(d)

About the Author

Hermann Weyl (1885-1955) is regarded as one of the greatest mathematicians of the twentieth century. Born and educated in Germany, he taught at the Institute for Advanced Study in Princeton, New Jersey, from 1933 until his retirement in 1951. He published five books with Princeton University Press, including Symmetry and The Classical Groups. Frank Wilczek is the Herman Feshbach Professor of Physics at Massachusetts Institute of Technology and the recipient of the 2004 Nobel Prize in Physics.

Table of Contents

Introduction vii

Preface xv

Bibliographical Note xvii

Part I Mathematics 1

Chapter I Mathematical Logic, Axiomatics 3

1 Relations and their Combination, Structure of Propositions

2 The Constructive Mathematical Definition

3 Logical Inference

4 The Axiomatic Method

Chapter II Number and Continuum, the Infinite 30

5 Rational Numbers and Complex Numbers

6 The Natural Numbers

7 The Irrational and the Infinitely Small

8 Set Theory

9 Intuitive Mathematics

10 Symbolic Mathematics

11 On the Character of Mathematical Cognition

Chapter III Geometry 67

12 Non-Euclidean, Analytic, Multi-dimensional, Affine, Projective Geometry; the Color Space

13 The Problem of Relativity

14 Congruence and Similarity. Left and Right

15 Riemann's Point of View. Topology

Part II Natural Science 93

Chapter I Space and Time, the Transcendental External World 95

16 The Structure of Space and Time in their Physical Effectiveness

17 Subject and Object (The Scientific Implications of Epistemology)

18 The Problem of Space

Chapter II Methodology 139

19 Measuring

20 Formation of Concepts

21 Formation of Theories

Chapter III The Physical Picture of the World 165

22 Matter

23 Causality (Law, Chance, Freedom)

Appendices 219

Appendix A The Structure of Mathematics 219

Appendix B Ars Combinatoria 237

Appendix C Quantum Physics and Causality 253

Appendix D Chemical Valence and the Hierarchy of Structures 266

Appendix E Physics and Biology 276

Appendix F The Main Features of the Physical World; Morphe and Evolution 285

Index 302

Editorial Reviews

"The translation has long been out of print, so this recent publication, with a very fine introduction by Frank Wilczek, is to be highly valued. . . . Weyl's Philosophy of Mathematics and Natural Science should be on every mathematician's or physicist's bookshelf. . . . What a pleasure, what a privilege, to read and contemplate Hermann Weyl's monumental achievements."—-Jeremy Butterfield, Physics Today

"[W]e remain ever grateful that Hermann Weyl, compromising his conscience to the extent that he did, left behind this unrivaled treasure of insights into the murkiest epistemological depths of mathematics and theoretical physics."—-Thomas Ryckman, Metascience

From the Publisher

[W]e remain ever grateful that Hermann Weyl, compromising his conscience to the extent that he did, left behind this unrivaled treasure of insights into the murkiest epistemological depths of mathematics and theoretical physics.

Metascience - Thomas Ryckman

The translation has long been out of print, so this recent publication, with a very fine introduction by Frank Wilczek, is to be highly valued. . . . Weyl's Philosophy of Mathematics and Natural Science should be on every mathematician's or physicist's bookshelf. . . . What a pleasure, what a privilege, to read and contemplate Hermann Weyl's monumental achievements.

Physics Today - Jeremy Butterfield

[W]e remain ever grateful that Hermann Weyl, compromising his conscience to the extent that he did, left behind this unrivaled treasure of insights into the murkiest epistemological depths of mathematics and theoretical physics.
— Thomas Ryckman

Metascience

The translation has long been out of print, so this recent publication, with a very fine introduction by Frank Wilczek, is to be highly valued. . . . Weyl's Philosophy of Mathematics and Natural Science should be on every mathematician's or physicist's bookshelf. . . . What a pleasure, what a privilege, to read and contemplate Hermann Weyl's monumental achievements.
— Jeremy Butterfield

Physics Today