Description
Book SynopsisExplores the central problems and the most intriguing new directions in the philosophy of mathematics. The papers are organized thematically, rather than chronologically, to give the best overview of philosophical issues connected with mathematics and the development of mathematical knowledge.
Trade Review"For breadth of coverage, Jacquette's anthology of recent work in philosophy of mathematics has few if any rivals. Many of Jacquette's selections are important for understanding current debates, and he provides helpful introductory discussions. This collection will very likely become a standard resource for students and teachers of this field."
Sanford Shieh, Wesleyan University Table of ContentsPreface.
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.
