Proofs and Refutations - The Logic of Mathematical Discovery

Chapter 1
1. A problem and a conjecture
2. A proof
3. Criticism of the proof by counterexamples which are local but not global
4. Criticism of the conjecture by global counterexamples
5. Criticism of the proof-analysis by counterexamples which are global but not local. The problem of rigour
6. Return to criticism of the proof by counterexamples which are local but nog global. The problem of content
7. The problem of content revisited
8. Concept-formation
9. How criticism may turn mathematical truth into logical truth
Chapter 2
1. Translation of the conjecture into the 'perfectly known' terms of vector-algebra. The problem of translation
2. Another proof of the conjecture
3. Some doubts about the finality of the proof. Translation procedure and the essentialist versus the nominalist approach to definitions
Appendix 1: Another case-study in the method of proofs and refutations
Appendix 2: The deductivist versus the heuristic approach