DescriptionThis distinctive anthology explores the central problems and exposes intriguing new directions in the philosophy of mathematics.
Introduction: Mathematics and Philosophy of Mathematics: Dale Jacquette.
Part I: The Realm of Mathematics:.
1. What is Mathematics About?: Michael Dummett.
2. Mathematical Explanation: Mark Steiner.
3. Frege versus Cantor and Dedekind: On the Concept of Number: William W. Tait.
4. The Present Situation in Philosophy of Mathematics: Henry Mehlberg.
Part II: Ontology of Mathematics and the Nature and Knowledge of Mathematical Truth:.
5. What Numbers Are: N.P. White.
6. Mathematical Truth: Paul Benacerraf.
7. Ontology and Mathematical Truth: Michael Jubien.
8. An Anti-Realist Account of Mathematical Truth: Graham Priest.
9. What Mathematical Knowledge Could Be: Jerrold J. Katz.
10. The Philosophical Basis of our Knowledge of Number: William Demonpoulos.
Part III: Models and Methods of Mathematical Proof:.
11. Mathematical Proof: G.H. Hardy.
12. What Does a Mathematical Proof Prove?: Imre Lakatos.
13. The Four-Color Problem: Kenneth Appel and Wolfgang Haken.
14. Knowledge of Proofs: Peter Pagin.
15. The Phenomenology of Mathematical Proof: Gian-Carlo Rota.
16. Mechanical Procedures and Mathematical Experience: Wilfried Sieg.
Part IV: Intuitionism:.
17. Intuitionism and Formalism: L.E.J. Brouwer.
18. Mathematical Intuition: Charles Parsons.
19. Brouwerian Intuitionism: Michael Detlefsen.
20. A Problem for Intuitionism: The Apparent Possibility of Performing Infinitely Many Tasks in a Finite Time: A.W. Moore.
21. A Pragmatic Analysis of Mathematical Realism and Intuitionism: Michel J. Blais.
Part V: Philosophical Foundations of Set Theory:.
22. Sets and Numbers: Penelope Maddy.
23. Sets, Aggregates, and Numbers: Palle Yourgrau.
24. The Approaches to Set Theory: John Lake.
25. Where Do Sets Come From? Harold T. Hodes.
26. Conceptual Schemes in Set Theory: Robert McNaughton.
27. What is Required of a Foundation for Mathematics? John Mayberry.
- Explores the central problems and exposes intriguing new directions in the philosophy of mathematics
- Includes many of the most important recent contributions to the philosophy of mathematics
- Presents information thematically, rather than chronologically, to provide the best overview of philosophical issues connected with mathematics and the development of mathematical knowledge