This volume brings together a selection of Solomon Feferman's most important recent writings, covering the relation between logic and mathematics, proof theory, objectivity and intensionality in mathematics, and key issues in the work of Gödel, Hilbert, and Turing.

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

"...the papers in this book provide an illuminating picture of much of the past work and a good deal of current progress in the foundations of mathematics. The author, one of the most distinguished contributors to that progress within the last four decades, is an excellent expositor of the various issues in the forefront of recent research..."--Mathematical Reviews