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

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

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 t...

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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
Online Access:
Physical Description:1 online resource (256 p.) :; 3 halftones. 14 line illus.
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245 1 0 |a Making and Breaking Mathematical Sense :  |b Histories and Philosophies of Mathematical Practice /  |c Roi Wagner. 
264 1 |a Princeton, NJ :   |b Princeton University Press,   |c [2017] 
264 4 |c ©2017 
300 |a 1 online resource (256 p.) :  |b 3 halftones. 14 line illus. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
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505 0 0 |t Frontmatter --   |t Contents --   |t Acknowledgments --   |t Introduction --   |t Chapter 1: Histories of Philosophies of Mathematics --   |t Chapter 2: The New Entities of Abbacus and Renaissance Algebra --   |t Chapter 3: A Constraints-Based Philosophy of Mathematical Practice --   |t Chapter 4: Two Case Studies of Semiosis in Mathematics --   |t Chapter 5: Mathematics and Cognition --   |t Chapter 6: Mathematical Metaphors Gone Wild --   |t Chapter 7: Making a World, Mathematically --   |t Bibliography --   |t Index 
506 0 |a restricted access  |u http://purl.org/coar/access_right/c_16ec  |f online access with authorization  |2 star 
520 |a 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. 
530 |a Issued also in print. 
538 |a Mode of access: Internet via World Wide Web. 
546 |a In English. 
588 0 |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021) 
650 0 |a Mathematics  |x History. 
650 0 |a Mathematics  |x Philosophy  |x History. 
650 7 |a MATHEMATICS / History & Philosophy.  |2 bisacsh 
653 |a Benedetto. 
653 |a Black-Scholes formula. 
653 |a Eugene Wigner. 
653 |a Friedrich W.J. Schelling. 
653 |a George Lakoff. 
653 |a Gilles Deleuze. 
653 |a Hermann Cohen. 
653 |a Hilary Putnam. 
653 |a Johann G. Fichte. 
653 |a Logic of Sensation. 
653 |a Mark Steiner. 
653 |a Rafael Nez. 
653 |a Stanislas Dehaene. 
653 |a Vincent Walsh. 
653 |a Water J. Freeman III. 
653 |a abbaco. 
653 |a algebra. 
653 |a arithmetic. 
653 |a authority. 
653 |a cognitive theory. 
653 |a combinatorics. 
653 |a conceptual freedom. 
653 |a constraints. 
653 |a economy. 
653 |a gender role stereotypes. 
653 |a generating functions. 
653 |a geometry. 
653 |a inferences. 
653 |a infinities. 
653 |a infinity. 
653 |a mathematical cognition. 
653 |a mathematical concepts. 
653 |a mathematical cultures. 
653 |a mathematical domains. 
653 |a mathematical entities. 
653 |a mathematical evolution. 
653 |a mathematical interpretation. 
653 |a mathematical language. 
653 |a mathematical metaphor. 
653 |a mathematical norms. 
653 |a mathematical objects. 
653 |a mathematical practice. 
653 |a mathematical signs. 
653 |a mathematical standards. 
653 |a mathematical statements. 
653 |a mathematics. 
653 |a natural order. 
653 |a natural sciences. 
653 |a nature. 
653 |a negative numbers. 
653 |a number sense. 
653 |a option pricing. 
653 |a philosophy of mathematics. 
653 |a reality. 
653 |a reason. 
653 |a relevance. 
653 |a semiosis. 
653 |a sexuality. 
653 |a stable marriage problem. 
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776 0 |c print  |z 9780691171715 
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