Table of Contents

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

Reviews

"...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