Making and Breaking Mathematical Sense ：Histories and Philosophies of Mathematical Practice

Publication subTitle ：Histories and Philosophies of Mathematical Practice

Author： Wagner Roi

Publisher： Princeton University Press‎

Publication year： 2017

E-ISBN: 9781400883783

P-ISBN(Paperback): 9780691171715

Subject： B Philosophy and Religion;N09 History;O1 Mathematics

Keyword：自然科学史,自然科学理论与方法论,哲学、宗教,数学

Language： ENG

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Description

In line with the emerging field of philosophy of mathematical practice, this book pushes the philosophy of mathematics away from questions about the reality and truth of mathematical entities and statements and toward a focus on what mathematicians actually do—and how that evolves and changes over time. How do new mathematical entities come to be? What internal, natural, cognitive, and social constraints shape mathematical cultures? How do mathematical signs form and reform their meanings? How can we model the cognitive processes at play in mathematical evolution? And how does mathematics tie together ideas, reality, and applications?

Roi Wagner uniquely combines philosophical, historical, and cognitive studies to paint a fully rounded image of mathematics not as an absolute ideal but as a human endeavor that takes shape in specific social and institutional contexts. The book builds on ancient, medieval, and modern case studies to confront philosophical reconstructions and cutting-edge cognitive theories. It focuses on the contingent semiotic and interpretive dimensions of mathematical practice, rather than on mathematics’ claim to universal or fundamental truths, in order to explore not only what mathematics is, but also what it could be. Along the way, Wagner challenges conventional views that mathematical signs represent fixed, ideal entities; that mathematical cognition is a rigid transfer of inferences between formal domains; and that mathematics