The Philosophy of Mathematical Practice

Paperback | December 8, 2011

EditorPaolo Mancosu

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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 andphilosophy 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 inphilosophy 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 foundationaldebates. 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 eighttopics 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 ofcategory theory; philosophical aspects of computer science in mathematics; the philosophical impact of recent developments in mathematical physics.

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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 andphilosophy of mathematics. But anyone familiar...

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...

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Format:PaperbackDimensions:464 pagesPublished:December 8, 2011Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199640106

ISBN - 13:9780199640102

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Table of Contents

Paolo Mancosu: Introduction1. Marcus Giaquinto: Visualization2. Kenneth Manders: Diagrammatic Reasoning and Representational Systems3. Paolo Mancosu and Johannes Hafner: Explanation4. Mic Detlefsen and Michael Hallett: Purity of Methods5. James Tappenden: Mathematical concepts6. Colin McLarty: Philosophical Relevance of Category Theory7. Jeremy Avigad: Philosophical Relevance of Computers in Mathematics8. Alasdair Urquhart: Philosophical Relevance of the interaction between mathematical physics and pure mathematics

Editorial Reviews

Review from previous edition: "highly commendable to a large pool of readers ... All taken together, this carefully produced book will be of great interest to those who care for the philosophy of mathematics." --History and Philosophy of Logic