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In the Light of Logic
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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
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Subject categories
- Academic > Mathematics > General > Logic, Symbolic and mathematical
- Academic > Mathematics > General > Logic, Symbolic and mathematical; Methodology
- Academic > Mathematics > Instruments and machines
- Academic > Mathematics > Analytic mechanics
- Academic > Logic > Logic, Symbolic and mathematical; Methodology
- Academic > Computer Science
- Mathematics > History & Philosophy
- Philosophy
ISBNs
0195359836
9780195080308
9780195359831