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Proofs and Refutations: The Logic of Mathematical Discovery
Table of ContentsEditors' preface; Acknowledgments; Author's introduction; 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 not global: the problem of content; 7. The problem of content revisited; 8. Concept-formation; 9. How criticism may turn mathematical truth into logical truth; Appendices; Bibliography; Index of names; Index of subjects.