Acknowledgments.

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.

Index.