| Preface | |
| Introduction | |
| The Structuralist Approach | p. 1 |
| The Special Role of Mathematics | p. 7 |
| Plato's Lecture on The Good | p. 8 |
| General Structure Concepts | |
| The Definition Problem | p. 11 |
| Structuralist Notions of Structure | p. 11 |
| A Simple Example | p. 15 |
| The Basic Definitions | p. 17 |
| Isomorphisms of Structures | p. 21 |
| Analogies and Isomorphisms | p. 23 |
| An Analysis of Point-Line Structures | p. 27 |
| Special Kinds of Relations | p. 29 |
| Structural Stability | p. 30 |
| Structural Information | p. 33 |
| On Abstract Structures | p. 35 |
| Some Examples of Structures | |
| Atoms and Machines | p. 40 |
| Line Drawings by Josef Albers | p. 42 |
| Configurations | p. 44 |
| The Pascal Configuration | p. 46 |
| The Triangle Group | p. 48 |
| Group Structures | p. 50 |
| The Real Number System | p. 54 |
| Management of Complex Structures | |
| The Analysis of Structures | p. 57 |
| The Approximation of Structures | p. 58 |
| Axiomatics and Approximation | p. 58 |
| Structural Determinism and Reductionism | p. 60 |
| Contractions | p. 65 |
| Contraction of Group Structures | p. 71 |
| Language and Structure | |
| The Role of Language | p. 73 |
| Simple Communication | p. 75 |
| Structural Linguistics | p. 77 |
| Semiotics | p. 82 |
| The Language Faculty | p. 88 |
| Structures in Mental Phenomena | |
| The Central Role of Structures | p. 94 |
| The Drive for Intelligibility | p. 97 |
| Philosophical Questions | p. 100 |
| The Background Structure and Understanding | p. 105 |
| Teaching and Learning | p. 108 |
| Mathematical Structures | |
| Mathematical Language | p. 116 |
| How to Recognize a Mathematical Structure | p. 119 |
| Research and Development of Mathematics | p. 120 |
| The Role of Insight in Research | p. 122 |
| A Structural Interpretation of Creativity | p. 128 |
| How Mathematics is Applied | p. 131 |
| The Effectiveness of Mathematics in Physics | p. 133 |
| Other Applications of Mathematics | p. 138 |
| Biological Structures | |
| Classification of Organisms | p. 146 |
| The Genetic Structure | p. 148 |
| The Environment of a Structure | p. 152 |
| The Evolutionary Process | p. 153 |
| Complexity in Evolution | p. 157 |
| Multiple Function | p. 163 |
| Biological Catastrophes | p. 168 |
| Determining Structures | p. 173 |
| Convergent Evolution | p. 174 |
| Anthropomorphism | p. 175 |
| Space Structures and Stability | |
| Euclidean Spaces | p. 180 |
| Substructures of Euclidean Space | p. 181 |
| The Conic Sections | p. 182 |
| Stability in a Family of Conics | p. 186 |
| Catastrophe Theory | p. 188 |
| Zeeman's Catastrophe Machine | p. 190 |
| A Mathematical Example | p. 191 |
| Attack or Retreat | p. 196 |
| Metric Spaces | p. 199 |
| Stability of Point-Line Structures | p. 201 |
| Bibliography | p. 207 |
| Index | p. 211 |
| Table of Contents provided by Blackwell. All Rights Reserved. |