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More About This Textbook
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.
Editorial Reviews
Physics Today
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
Metascience
[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
Physics Today - Jeremy Butterfield
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.Metascience - Thomas Ryckman
[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.Product Details
Meet 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