This distinctive anthology includes many of the most important recent contributions to the philosophy of mathematics. The featured papers are organized thematically, rather than chronologically, to provide the best overview of philosophical issues connected with mathematics and the development of mathematical knowledge. Coverage ranges from general topics in mathematical explanation and the concept of number, to specialized investigations of the ontology of mathematical entities and the nature of mathematical truth, models and methods of mathematical proof, intuitionistic mathematics, and philosophical foundations of set theory. This volume explores the central problems and exposes intriguing new directions in the philosophy of mathematics, making it an essential teaching resource, reference work, and research guide. The book complements Philosophy of Logic: An Anthology and A Companion to Philosophical Logic, also edited by Dale Jacquette (Blackwell 2001).
Dale Jacquette is Professor of Philosophy at The Pennsylvania State University. He is the author of Philosophy of Mind (1994), Meinongian Logic: The Semantics of Existence and Nonexistence (1996), Wittgenstein's Thought in Transition (1998), Symbolic Logic (2001), David Hume's Critique of Infinity (2001) and On Boole: Logic as Algebra (2001) as well as numerous articles on logic, metaphysics, philosophy of mind, and Wittgenstein.
Preface. 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.