Making and Breaking Mathematical Sense : : Histories and Philosophies of Mathematical Practice / / Roi Wagner.

• Superior document: Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2017
• VerfasserIn: Wagner, Roi,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2017]; ©2017
• Year of Publication: 2017
• Language: English
• Physical Description: 1 online resource (256 p.) :; 3 halftones. 14 line illus.

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' exceptional consensus is due to the subject's underlying reality.The result is a revisionist account of mathematical philosophy that will interest mathematicians, philosophers, and historians of science alike.

Table of Contents

Frontmatter -- Contents -- Acknowledgments -- Introduction -- Chapter 1: Histories of Philosophies of Mathematics -- Chapter 2: The New Entities of Abbacus and Renaissance Algebra -- Chapter 3: A Constraints-Based Philosophy of Mathematical Practice -- Chapter 4: Two Case Studies of Semiosis in Mathematics -- Chapter 5: Mathematics and Cognition -- Chapter 6: Mathematical Metaphors Gone Wild -- Chapter 7: Making a World, Mathematically -- Bibliography -- Index