The Philosophy of Mathematical Practice

Contemporary philosophy of mathematics offers us an embarrassment of riches. Among the major areas of work one could list developments of the classical foundational programs, analytic approaches to epistemology and ontology of mathematics, and developments at the intersection of history and philosophy of mathematics. But anyone familiar with contemporary philosophy of mathematics will be aware of the need for new approaches that pay closer attention to mathematical practice. This book is the first attempt to give a coherent and unified presentation of this new wave of work in philosophy of mathematics. The new approach is innovative at least in 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 which escape purely formal logical treatment--such as visualization, explanation, and understanding--can nonetheless be subjected to philosophical analysis. The Philosophy of Mathematical Practice comprises an introduction by the editor and eight chapters written by some of the leading scholars in the field. Each chapter consists of a short introduction to the general topic of the chapter followed by a longer research article in the area. The eight topics selected represent a broad spectrum of contemporary philosophical reflection on different aspects of mathematical practice: diagrammatic reasoning and representational systems; visualization; mathematical explanation; purity of methods; mathematical concepts; the philosophical relevance of category theory; philosophical aspects of computer science in mathematics; the philosophical impact of recent developments in mathematical physics.

Paolo Mancosu is Professor of Philosophy at University of California, Berkeley. His main interests are in logic, history and philosophy of mathematics, and history and philosophy of logic. He is the author of Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century and editor of From Brouwer to Hilbert: The debate on the foundations of mathematics in the 1920s . He has recently co-edited the volume Visualization, Explanation and Reasoning Styles in Mathematics ). He is currently working on mathematical explanation and on Tarskian themes (truth, logical consequence, logical constants, nominalism) in philosophy of logic.

Introduction, Paolo Mancosu
1. Visualization, Marcus Giaquinto
2. Diagrammatic Reasoning and Representational Systems, Kenneth Manders
3. Explanation, Paolo Mancosu and Johannes Hafner
4. Purity of Methods, Mic Detlefsen and Michael Hallett
5. Mathematical concepts, James Tappenden
6. Philosophical Relevance of Category Theory, Colin McLarty
7. Philosophical Relevance of Computers in Mathematics, Jeremy Avigad
8. Philosophical Relevance of the interaction between mathematical physics and pure mathematics, Alasdair Urquhart