Proof and Other Dilemmas: Mathematics and Philosophy

Acknowledgments Introduction Part I. Proof and How it is Changing: 1. Proof: its nature and significance Michael Detlefsen 2. Implications of experimental mathematics for the philosophy of mathematics Jonathan Borwein 3. On the roles of proof in mathematics Joseph Auslander Part II. Social Constructivist Views of Mathematics: 4. When is a problem solved? Philip J. Davis 5. Mathematical practice as a scientific problem Reuben Hersh 6. Mathematical domains: social constructs? Julian Cole Part III. The Nature of Mathematical Objects and Mathematical Knowledge: 7. The existence of mathematical objects Charles Chihara 8. Mathematical objects Stewart Shapiro 9. Mathematical Platonism Mark Balaguer 10. The nature of mathematical objects Oystein Linnebo 11. When is one thing equal to some other thing? Barry Mazur Part IV. The Nature of Mathematics and its Applications: 12. Extreme science: mathematics as the science of relations as such R. S. D. Thomas 13. What is mathematics? A pedagogical answer to a philosophical question Guershon Harel 14. What will count as mathematics in 2100? Keith Devlin 15. Mathematics applied: the case of addition Mark Steiner 16. Probability - a philosophical overview Alan Hajek Glossary of common philosophical terms About the editors.