an outstanding collection, highly informative, sometimes provocative, often insightful, and throughout displaying the great clarity and command which are hallmarks of the author's writing.

• I: FOUNDATIONAL PROBLEMS ; 1. Declining the undecidable: Wrestling with Hilbert's Problems ; 2. Infinity in Mathematics: Is Cantor necessary? ; 3. The logic of mathematical discovery vs. the logical structure of mathematics ; II: FOUNDATIONAL WAYS ; 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 1993 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

an outstanding collection, highly informative, sometimes provocative, often insightful, and throughout displaying the great clarity and command which are hallmarks of the author's writing.

• I: FOUNDATIONAL PROBLEMS ; 1. Declining the undecidable: Wrestling with Hilbert's Problems ; 2. Infinity in Mathematics: Is Cantor necessary? ; 3. The logic of mathematical discovery vs. the logical structure of mathematics ; II: FOUNDATIONAL WAYS ; 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 1993 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

an outstanding collection, highly informative, sometimes provocative, often insightful, and throughout displaying the great clarity and command which are hallmarks of the author's writing.

• I: FOUNDATIONAL PROBLEMS ; 1. Declining the undecidable: Wrestling with Hilbert's Problems ; 2. Infinity in Mathematics: Is Cantor necessary? ; 3. The logic of mathematical discovery vs. the logical structure of mathematics ; II: FOUNDATIONAL WAYS ; 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 1993 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