Why Is There Philosophy of Mathematics At All?

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.

Table of Contents

Chapter 1. A cartesian introduction

Chapter 2. What makes mathematics mathematics?

Chapter 3. Why is there philosophy of mathematics?

Chapter 4. Proofs

Chapter 5. Applications

Chapter 6. In Plato’s name

Chapter 7 Counter-platonisms

Review

“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

“… readable, presented in easily digestible chunks, clearly explained, and just a lot of fun …”

Danny Yee’s Book Reviews

“Show[s] non-specialists … the sort of distinctive contribution to science and maths that a brilliant, very well-informed, philosopher can bring … I thoroughly recommend this book.”

Alan Weir, The Times Literary Supplement

“Hacking has composed a great overview of our understanding of mathematics and of the historical turning points and philosophical basics.”

Peeter Müürsepp, Mathematical Reviews

Book Description

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

About the Author

Ian Hacking is a retired professor of Collège de France, Chair of Philosophy and History of Scientific Concepts, and retired University Professor of Philosophy at the University of Toronto. His most recent books include The Social Construction of What? (1999), An Introduction to Probability and Inductive Logic (Cambridge University Press, 2001), The Emergence of Probability (Cambridge University Press, 2006), Scientific Reason (2009) and Exercises in Analysis (Cambridge University Press, 2009).