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