There is an urgent need in philosophy of mathematics for new approaches which pay closer attention to mathematical practice. This book will blaze the trail: it offers philosophical analyses of important characteristics of contemporary mathematics and of many aspects of mathematical activity which escape purely formal logical treatment.

• Introduction


• 1: Marcus Giaquinto: Visualization


• 2: Kenneth Manders: Diagrammatic Reasoning and Representational Systems


• 3: Paolo Mancosu and Johannes Hafner: Explanation


• 4: Mic Detlefsen and Michael Hallett: Purity of Methods


• 5: James Tappenden: Mathematical concepts


• 6: Colin McLarty: Philosophical Relevance of Category Theory


• 7: Jeremy Avigad: Philosophical Relevance of Computers in Mathematics


• 8: Alasdair Urquhart: Philosophical Relevance of the interaction between mathematical physics and pure mathematics

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 (OUP 1996) and editor of From Brouwer to Hilbert: The debate on the foundations of mathematics in the 1920s (OUP 1988). He has recently co-edited the volume Visualization, Explanation and Reasoning Styles in Mathematics (Springer 2005). He is currently working on mathematical explanation and on Tarskian themes (truth, logical consequence, logical constants, nominalism) in philosophy of logic.