Why Is There Philosophy of Mathematics At All?

Hacking explores how mathematics became possible for the human race, and how it ensured our status as the dominant species.

Ian Hacking (Author)

9781107050174, Cambridge University Press

Hardback, published 30 January 2014

308 pages
22.9 x 15.2 x 2.1 cm, 0.62 kg

'Hacking has composed a great overview of our understanding of mathematics and of the historical turning points and philosophical basics.' Peeter Müürsepp, Mathematical Reviews

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.

Subject Areas: Philosophy of science [PDA], Mathematical logic [PBCD], Philosophy of mathematics [PBB], Philosophy [HP]