TABLE OF CONTENTS: Introduction 1
I.1 Opening Remarks 1
I.2 Some Mathematical Concepts 16
CHAPTER 1: Modernism and Mathematics 18
1.1 Modernism in Branches of Mathematics 18
1.2 Changes in Philosophy 24
1.3 The Modernization of Mathematics 32
CHAPTER 2: Before Modernism 39
2.1 Geometry 39
2.2 Analysis 58
2.3 Algebra 75
2.4 Philosophy 78
2.5 British Algebra and Logic 101
2.6 The Consensus in 1880 112
CHAPTER 3: Mathematical Modernism Arrives 113
3.1 Modern Geometry: Piecemeal Abstraction 113
3.2 Modern Analysis 129
3.3 Algebra 148
3.4 Modern Logic and Set Theory 157
3.5 The View from Paris and St. Louis 170
CHAPTER 4: Modernism Avowed 176
4.1 Geometry 176
4.2 Philosophy and Mathematics in Germany 196
4.3 Algebra 213
4.4 Modern Analysis 216
4.5 Modernist Objects 235
4.6 American Philosophers and Logicians 239
4.7 The Paradoxes of Set Theory 247
4.8 Anxiety 266
4.9 Coming to Terms with Kant 277
CHAPTER 5: Faces of Mathematics 305
5.1 Introduction 305
5.2 Mathematics and Physics 306
5.3 Measurement 328
5.4 Popularizing Mathematics around 1900 346
5. Writing the History of Mathematics 365
CHAPTER 6: Mathematics, Language, and Psychology 374
6.1 Languages Natural and Artificial 374
6.2 Mathematical Modernism and Psychology 388
CHAPTER 7: After the War 406
7.1 The Foundations of Mathematics 406
7.2 Mathematics and the Mechanization of Thought 430
7.3 The Rise of Mathematical Platonism 440
7.4 Did Modernism'"Win"? 452
7.5 The Work Is Done 458
Appendix: Four Theorems in Projective Geometry 463
Glossary 467
Bibliography 473
Index 503
Return to Book Description File created: 11/5/2009 | 
