In this book, thirteen promising young researchers write on what they take to be the right philosophical account of mathematics and discuss where the philosophy of mathematics ought to be going. New trends are revealed, such as an increasing attention to mathematical practice, a reassessment of the canon, and inspiration from philosophical logic.
Author(s): Otavio Bueno, Oystein Linnebo
Publisher: Palgrave Macmillan
Year: 2009
Language: English
Pages: 338
Cover......Page 1
Contents......Page 6
Series Editors’ Foreword......Page 8
Acknowledgements......Page 9
List of Contributors......Page 10
Philosophy of Mathematics: Old and New......Page 12
Part I: Reassessing the Orthodoxy in the Philosophy of Mathematics......Page 22
1 New Waves on an Old Beach: Fregean Philosophy of Mathematics Today......Page 24
2 Reducing Arithmetic to Set Theory......Page 46
Part II: The Question of Realism in Mathematics......Page 68
3 Mathematical Fictionalism......Page 70
4 Truth in Mathematics: The Question of Pluralism......Page 91
5 “Algebraic” Approaches to Mathematics......Page 128
Part III: Mathematical Practice and the Methodology of Mathematics......Page 146
6 Mathematical Accidents and the End of Explanation......Page 148
7 Applying Inconsistent Mathematics......Page 171
8 Towards a Philosophy of Applied Mathematics......Page 184
Part IV: Mathematical Language and the Psychology of Mathematics......Page 206
9 Formal Tools and the Philosophy of Mathematics......Page 208
10 The Individuation of the Natural Numbers......Page 231
11 Toward a Trivialist Account of Mathematics......Page 250
Part V: From Philosophical Logic to the Philosophy of Mathematics......Page 272
12 On Formal and Informal Provability......Page 274
13 Quantification Without a Domain......Page 311
D......Page 335
I......Page 336
P......Page 337
Z......Page 338
