The Philosophy of Mathematical Practice Reviewed by Timothy Bays
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چکیده
For mathematicians, modern philosophy of mathematics may seem somewhat puzzling. In the late nineteenth and early twentieth centuries, the borders between philosophy and mathematics were porous. Influential mathematicians like Poincaré, Brouwer, Ramsey, and Hilbert wrote extensively on philosophical topics, and philosophers like Russell, Wittgenstein, and Quine made serious philosophical use of contemporaneous mathematics. More importantly, the issues that concerned philosophers of mathematics were often continuous with developments in mathematics proper—e.g., the rigorization of analysis in the nineteenth century, the discovery of the settheoretic paradoxes and Gödel’s incompleteness theorems, or Bourbaki’s project of systematizing mathematics as a whole. In recent years, mathematics and the philosophy of mathematics have become somewhat more distant. The topics that most exercise philosophers of mathematics—realism and anti-realism, the metaphysics of structuralism, or arguments concerning the indispensability of mathematics to natural science—don’t connect very well with the day-to-day concerns of practicingmathematicians. This is not to say that philosophy of mathematics has become insular and unmotivated. It’s just
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