In the Light of Logic

Title ......Page 3
Copyright ......Page 4
Dedication ......Page 5
Preface ......Page 7
Contents ......Page 11
I. FOUNDATIONAL PROBLEMS ......Page 13
1. Deciding the undecidable: Wrestling with Hilbert\'s problems ......Page 15
2. Infinity in mathematics: Is Cantor necessary? ......Page 40
II. FOUNDATIONAL WAYS ......Page 87
3. The logic of mathematical discovery versus the logical structure of mathematics ......Page 89
4. Foundational ways ......Page 106
5. Working foundations ......Page 117
III. GODEL ......Page 137
6. Godel\'s life and work ......Page 139
7. Kurt Godel: Conviction and caution ......Page 162
8. Introductory note to Godel\'s 1933 lecture ......Page 177
IV. PROOF THEORY ......Page 187
9. What does logic have to tell us about mathematical proofs? ......Page 189
10. What rests on what? The proof-theoretic analysis of mathematics ......Page 199
11. Godel\'s Dialectica interpretation and its two-way stretch ......Page 221
V. COUNTABLY REDUCIBLE MATHEMATICS ......Page 239
12. Infinity in mathematics: Is Cantor necessary? (Conclusion) ......Page 241
13. Weyl vindicated: Das Kontinuum seventy years later ......Page 261
14. Why a little bit goes a long way: Logical foundations of scientifically applicable mathematics ......Page 296
Symbols ......Page 311
References ......Page 321
Index ......Page 343
Cover ......Page 353