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9780691141206

Philosophy of Mathematics and Natural Science

by ; ;
  • ISBN13:

    9780691141206

  • ISBN10:

    0691141207

  • Format: Paperback
  • Copyright: 2009-04-27
  • Publisher: Princeton Univ Pr

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Summary

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. InPhilosophy 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.

Author Biography

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, NJ, 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

Introductionp. vii
Prefacep. xv
Bibliographical Notep. xvii
Mathematicsp. 1
Mathematical Logic, Axiomaticsp. 3
Relations and their Combination, Structure of Propositions
The Constructive Mathematical Definition
Logical Inference
The Axiomatic Method
Number and Continuum, the Infinitep. 30
Rational Numbers and Complex Numbers
The Natural Numbers
The Irrational and the Infinitely Small
Set Theory
Intuitive Mathematics
Symbolic Mathematics
On the Character of Mathematical Cognition
Geometryp. 67
Non-Euclidean, Analytic, Multi-dimensional, Affine, Projective Geometry; the Color Space
The Problem of Relativity
Congruence and Similarity. Left and Right
Riemann's Point of View. Topology
Natural Sciencep. 93
Space and Time, the Transcendental External Worldp. 95
The Structure of Space and Time in their Physical Effectiveness
Subject and Object (The Scientific Implications of Epistemology)
The Problem of Space
Methodologyp. 139
Measuring
Formation of Concepts
Formation of Theories
The Physical Picture of the Worldp. 165
Matter
Causality (Law, Chance, Freedom)
Appendicesp. 219
The Structure of Mathematicsp. 219
Ars Combinatoriap. 237
Quantum Physics and Causalityp. 253
Chemical Valence and the Hierarchy of Structuresp. 266
Physics and Biologyp. 276
The Main Features of the Physical World; Morphe and Evolutionp. 285
Indexp. 302
Table of Contents provided by Ingram. All Rights Reserved.

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