Contents
Preface xi
A remark on notation xi
Acknowledgments xii
Chapter 1. Logic and foundations 1
§1.1. Material implication 1
§1.2. Errors in mathematical proofs 2
§1.3. Mathematical strength 4
§1.4. Stable implications 6
§1.5. Notational conventions 8
§1.6. Abstraction 9
§1.7. Circular arguments 11
§1.8. The classical number systems 12
§1.9. Round numbers 15
§1.10. The “no-self-defeating object” argument, revisited 16
§1.11. The “no-self-defeating object” argument, and the vagueness
paradox 28
§1.12. A computational perspective on set theory 35
Chapter 2. Group theory 51
§2.1. Torsors 51
§2.2. Active and passive transformations 54
§2.3. Cayley graphs and the geometry of groups 56
§2.4. Group extensions 62
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