Synopses & Reviews
"The hard won power ... to assess correctly the continuum of the natural numbers grew out of titanic struggles in the realm of mathematical logic in which Hermann Weyl took a leading part." — John Archibald Wheeler
Hermann Weyl (1885-1955) ranks among the most important mathematicians and physicists of this century. Though Weyl was not primarily a philosopher, his wide-ranging philosophical reflections on the formal and empirical sciences remain extremely valuable. Besides indicating clearly which results of classical analysis are invalidated by an important family of "non-circular" (predicative) theories, The Continuum wrestles with the problem of applying constructive mathematical models to cases of concrete physical and perceptual continuity. This new English edition features a personal reminiscence of Weyl written by John Archibald Wheeler.
Originally published in German in 1918, the book consists of two chapters. Chapter One, entitled Set and Function, deals with property, relation and existence, the principles of the combination of judgments, logical inference, natural numbers, iteration of the mathematical process, and other topics. The main ideas are developed in this chapter in such a way that it forms a self-contained whole.
In Chapter Two, The Concept of Numbers & The Continuum, Weyl systematically begins the construction of analysis and carries through its initial stages, taking up such matters as natural numbers and cardinalities, fractions and rational numbers, real numbers, continuous functions, curves and surfaces, and more.
Written with Weyl's characteristic passion, lucidity, and wisdom, this advanced-level volume is a mathematical and philosophical landmark that will be welcomed by mathematicians, physicists, philosophers, and anyone interested in foundational analysis.
Synopsis
This classic text deals with the conceptual problem posed by the continuum — the set of all real numbers. Chapter 1 deals with the logic and mathematics of set and function, while Chapter 2 focuses on the concept of number and the continuum. Advanced-level mathematical landmark will interest anyone working in foundational analysis. Bibliography. Originally published 1918.
Synopsis
This classic text deals with the conceptual problem posed by the continuum — the set of all real numbers. Chapter 1 deals with the logic and mathematics of set and function, while Chapter 2 focuses on the concept of number and the continuum. Advanced-level mathematical landmark will interest anyone working in foundational analysis. Bibliography. Originally published 1918.
Synopsis
Concise classic by great mathematician and physicist deals with logic and mathematics of set and function, concept of number and the continuum. Bibliography. Originally published 1918.
About the Author
Along with his fundamental contributions to most branches of mathematics, Hermann Weyl (1885-1955) took a serious interest in theoretical physics. In addition to teaching in Zürich, Göttingen, and Princeton, Weyl worked with Einstein on relativity theory at the Institute for Advanced Studies.
Hermann Weyl: The Search for Beautiful Truths
One of the most influential mathematicians of the twentieth century, Hermann Weyl (1885-1955) was associated with three major institutions during his working years: the ETH Zurich (Swiss Federal Institute of Technology), the University of Gottingen, and the Institute for Advanced Study in Princeton. In the last decade of Weyl's life (he died in Princeton in 1955), Dover reprinted two of his major works, The Theory of Groups and Quantum Mechanics and Space, Time, Matter. Two others, The Continuum and The Concept of a Riemann Surface were added to the Dover list in recent years.
In the Author's Own Words:
"My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful."
"We are not very pleased when we are forced to accept mathematical truth by virtue of a complicated chain of formal conclusions and computations, which we traverse blindly, link by link, feeling our way by touch. We want first an overview of the aim and of the road; we want to understand the idea of the proof, the deeper context."
"A modern mathematical proof is not very different from a modern machine, or a modern test setup: the simple fundamental principles are hidden and almost invisible under a mass of technical details." — Hermann Weyl
Critical Acclaim for Space, Time, Matter:
"A classic of physics . . . the first systematic presentation of Einstein's theory of relativity." — British Journal for Philosophy and Science
Table of Contents
Foreword; Introduction; Preface
Chapter 1. Set and Function
Logical Section
1. Property, Relation, Existence
2. The Principles of the combination of Judgments
3. Logical Inference. Axiomatic Method
Mathematical Section
4. Sets
5. The Natural Numbers: Richard's Antinomy
6. Iteration of the Mathematical Process. The circulus vitiosus of Analysis
7. Principles of Substitution and Iteration
8. Definitive Formulation of the Foundations. Introduction of Ideal Elements
Chapter 2. The Concept of Number and The Continuum
1. Natural Numbers and Cardinalities
2. Fractions and Rational Numbers
3. Real Numbers
4. Sequences, Convergence Principle
5. Continuous Functions
6. The Intuitive and the Mathematical Continuum
7. Magnitudes and Their Measures
8. Curves and Surfaces
Appendix; Notes; Bibliography; Index