The Philosophy of Mathematical Practice
Edited by Paolo Mancosu
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Philosophy of Mathematical Practice by Paolo Mancosu
Book DescriptionContemporary 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 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 representation 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.
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Book DetailsISBN: 9780199296453
(240mm x 165mm x 29mm)
Imprint: Oxford University Press
Publisher: Oxford University Press
Publish Date: 19-Jun-2008
Country of Publication: United Kingdom
Books By Author Paolo Mancosu
Abstraction and Infinity, Hardback (December 2016)
Mancosu offers an original investigation of key notions in mathematics: abstraction and infinity, and their interaction. He gives a historical analysis of the theorizing of definitions by abstraction, and explores a novel approach to measuring the size of infinite sets, showing how this leads to deep mathematical and philosophical problems.
Adventure of Reason, Paperback (January 2014)
Paolo Mancosu presents an innovative set of studies of logic and the foundations of mathematics in the first half of the twentieth century. He sheds new light on important topics such as the relationship between phenomenology and the exact sciences, the nature of truth and logical consequence, and the nature of mathematical intuition.
Philosophy of Mathematical Practice, Paperback (December 2011)» View all books by Paolo Mancosu
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.
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Author Biography - Paolo Mancosu
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.
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