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[HM] Philosophy of Real Mathematics
Posted:
May 6, 2003 4:35 AM


List members may be interested to learn that I have recently published a book, 'Towards a Philosophy of Real Mathematics', with Cambridge University Press . The book is based on my agreement with the second half of Lakatos's assertion in 'Proofs and Refutations' that:
The history of mathematics, lacking the guidance of philosophy, has become blind, while the philosophy of mathematics, turning its back on the most intriguing phenomena in the history of mathematics, has become empty.
1. Introduction: a role for history; Part I. Human and Artificial Mathematicians: 2. Communicating with automated theorem provers; 3. Automated conjecture formation; 4. The role of analogy; Part II. Mathematical Uncertainty: 5. Bayesianism in mathematics; 6. Uncertainty in mathematics and science; Part III. The Growth of Mathematics: 7. Lakatos's philosophy of mathematics; 8. The methodology of mathematical research programmes; 9. The importance of mathematical conceptualisation; Part IV. The Interpretation of Mathematics: 10. Higher dimensional algebra.
I'd certainly welcome any exchange on the first half of Lakatos's claim.
David Corfield, Faculty of Philosophy, 10 Merton St., Oxford OX1 4JJ, UK http://users.ox.ac.uk/~sfop0076/



