Proof and other dilemmas : mathematics and philosophy
This collection of sixteen original essays is the first to explore a range of new developments in the philosophy of mathematics, in a way mathematicians will understand. Coverage includes emerging questions in the field as well as recent thinking on classical ideas, all relevant to the teaching of mathematics.
Print Book, English, cop. 2008
Mathematical Association of America, Washington, D.C, cop. 2008
XXXII, 346 p. il
9780883855676, 0883855674
816555172
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 Øystein 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 Hájek; Glossary of common philosophical terms; About the editors.