If you have access to Oxford Scholarship Online, you can now read Mancosu’s excellent collection The Philosophy of Mathematical Practice via the internets.
Contemporary philosophy of mathematics offers us an embarrassment of riches. But anyone familiar with this area will be aware of the need for new approaches that will pay closer attention to mathematical practice. This book provides a unified presentation of this new wave of work in philosophy of mathematics. This new approach is innovative in at least two ways. First, it holds that there are important novel characteristics of contemporary mathematics that are just as worthy of philosophical attention as the distinction between constructive and non constructive mathematics at the time of the foundational debates. Secondly, it holds that many topics that escape purely formal logical treatment — such as visualization, explanation, and understanding — can be nonetheless be subjected to philosophical analysis. The book comprises an introduction and eight sections. Each section consists of a short introduction outlining the general topic followed by a related research article. The eight topics selected represent a broad spectrum of contemporary philosophical reflection on different aspects of mathematical practice: visualization, diagrammatic reasoning and representational systems, mathematical explanation, purity of methods, mathematical concepts, philosophical relevance of category theory, philosophical aspects of computer science in mathematics, philosophical impact of recent developments in mathematical physics.