In the Light of Logic

I: Foundational Problems 1. Deciding the undecidable: Wrestling with Hilbert's Problems 2. Infinity in mathematics: Is Cantor necessary? II: Foundational Ways 3. The logic of mathematical discovery vs. the logical structure of mathematics 4. Foundational Ways 5. Working Foundations III: Godel 6. Godel's life and work 7. Kurt Godel: conviction and caution 8. Introductory note to Godel's 1933 lecture IV: Proof Theory 9. What does logic have to tell us about mathematical proofs? 10. What rests on what? The proof-theoretic analysis of mathematics 11. Godel's Dialectica interpretation and its two-way stretch V: Countably Reducible Mathematics 12. Infinity in mathematics: Is Cantor necessary? (Conclusion) 13. Weyl vindicated: Das Kontinuum 70 years later 14. Why a little bit goes a long way: Logical Foundations of scientifically applicable mathematics