Why Is There Philosophy of Mathematics at All?by Ian Hacking.

Abstract

Some may be tempted to read the title of Ian Hacking’s latest book as a call to dismiss the philosophy of mathematics. This would be a mistake. Hacking does not think that philosophy of mathematics will ever go away, and it is this enduring appeal that motivates Hacking’s book. Hacking asks why mathematics has perennially fascinated philosophers, to the point that the philosophy of mathematics is not the philosophy of a special science — like the philosophy of physics or biology — but rather a central field of analytic philosophy. As with much of Hacking’s work, his latest book unfolds through the history of mathematics. None the less, Hacking emphasizes that he is not giving interpretations of the texts he discusses (hence his lower-case spelling of ‘leibnizian’ and ‘cartesian’). He does not advance a particular thesis in the philosophy of mathematics but rather asks how the central questions and enduring views in the field have come about. Hacking answers that philosophers’ enthusiasm for mathematics has two sources: proof and application.