Why Is There Philosophy of Mathematics At All?
Cambridge University Press, 3/31/2014
EAN 9781107658158, ISBN10: 1107658152
Paperback, 308 pages, 22.9 x 15.2 x 1.8 cm
Language: English
This truly philosophical book takes us back to fundamentals - the sheer experience of proof, and the enigmatic relation of mathematics to nature. It asks unexpected questions, such as 'what makes mathematics mathematics?', 'where did proof come from and how did it evolve?', and 'how did the distinction between pure and applied mathematics come into being?' In a wide-ranging discussion that is both immersed in the past and unusually attuned to the competing philosophical ideas of contemporary mathematicians, it shows that proof and other forms of mathematical exploration continue to be living, evolving practices - responsive to new technologies, yet embedded in permanent (and astonishing) facts about human beings. It distinguishes several distinct types of application of mathematics, and shows how each leads to a different philosophical conundrum. Here is a remarkable body of new philosophical thinking about proofs, applications, and other mathematical activities.
Foreword
1. A Cartesian introduction
2. What makes mathematics mathematics?
3. Why is there philosophy of mathematics?
4. Proofs
5. Applications
6. In Plato's name
7. Counter-Platonisms
Disclosures.
'Hacking does not restrict himself to the foundations of mathematics, but dares to cover both the breadth and the depth of mathematical philosophy.' Literary Review of Canada