LEADER 03820nam a22005175i 4500001 99125257762406421 005 20240708094202.0 006 m|||||o||d|||||||| 007 cr#cnu|||||||| 008 190523s2017 nju fo d z eng d 010 |z2016022844 019 (OCoLC)984687424 024 7 10.1515/9781400883783 |2doi 035 (CKB)3710000000918032 035 (MiAaPQ)EBC4778017 035 (StDuBDS)EDZ0001815924 035 (DE-B1597)479741 035 (OCoLC)968732589 035 (OCoLC)984687424 035 (DE-B1597)9781400883783 035 (MdBmJHUP)musev2_125632 035 (EXLCZ)993710000000918032 040 DE-B1597 |beng |cDE-B1597 |erda 041 0 eng 044 nju |cUS-NJ 050 4 QA8.4.W334 2017 072 7 MAT015000 |2bisacsh 072 7 PHI000000 |2bisacsh 072 7 SCI034000 |2bisacsh 082 0 510.1 |223 100 1 Wagner, Roi, |eauthor. 245 10 Making and Breaking Mathematical Sense : |bHistories and Philosophies of Mathematical Practice / |cRoi Wagner. 264 1 Princeton, NJ : |bPrinceton University Press, |c[2017] 264 4 |c©2017 300 1 online resource (251 pages) 336 text |2rdacontent 337 computer |2rdamedia 338 online resource |2rdacarrier 500 Previously issued in print: 2017. 521 Specialized. 588 0 Description based on online resource; title from PDF title page (publisher's Web site, viewed 23. Mai 2019) 546 In English. 530 Issued also in print. 504 Includes bibliographical references (pages 219-231) and index. 505 0 Cover; Title; Copyright; Dedication; Contents; Acknowledgments; Introduction; What Philosophy of Mathematics Is Today; What Else Philosophy of Mathematics Can Be; A Vignette: Option Pricing and the Black-Scholes Formula; Outline of This Book; Chapter 1: Histories of Philosophies of Mathematics; History 1: On What There Is, Which Is a Tension between Natural Order and Conceptual Freedom; History 2: The Kantian Matrix, Which Grants Mathematics a Constitutive Intermediary Epistemological Position; History 3: Monster Barring, Monster Taming, and Living with Mathematical Monsters. 505 0 History 4: Authority, or Who Gets to Decide What Mathematics Is AboutThe "Yes, Please!" Philosophy of Mathematics; Chapter 2: The New Entities of Abbacus and Renaissance Algebra; Abbacus and Renaissance Algebraists; The Emergence of the Sign of the Unknown; First Intermediary Reflection; The Arithmetic of Debited Values; Second Intermediary Reflection; False and Sophistic Entities; Final Reflection and Conclusion; Chapter 3: A Constraints-Based Philosophy of Mathematical Practice; Dismotivation; The Analytic A Posteriori; Consensus; Interpretation; Reality; Constraints; Relevance; Conclusion. 505 0 Chapter 4: Two Case Studies of Semiosis in MathematicsAmbiguous Variables in Generating Functions; Between Formal Interpretations; Models and Applications; Openness to Interpretation; Gendered Signs in a Combinatorial Problem; The Problem; Gender Role Stereotypes and Mathematical Results; Mathematical Language and Its Reality; The Forking Paths of Mathematical Language; Chapter 5: Mathematics and Cognition; The Number Sense; Mathematical Metaphors; Some Challenges to the Theory of Mathematical Metaphors; Best Fit for Whom?; What Is a Conceptual Domain?; In Which Direction Does the Theory Go? 505 0 So How Should We Think about Mathematical Metaphors?An Alternative Neural Picture; Another Vision of Mathematical Cognition; From Diagrams to Haptic Vision; Haptic Vision in Practice; Chapter 6: Mathematical Metaphors Gone Wild; What Passes between Algebra and Geometry; Piero della Francesca (Italy, Fifteenth Century); Omar Khayyam (Central Asia, Eleventh Century); Rene Descartes (France, Seventeenth Century); Rafael Bombelli (Italy, Sixteenth Century); Conclusion; A Garden of Infinities; Limits; Infinitesimals and Actual Infinities; Chapter 7: Making a World, Mathematically; Fichte. 505 0 SchellingHermann Cohen; The Unreasonable Applicability of Mathematics; Bibliography; Index. 520 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. 650 0 Mathematics |xPhilosophy |xHistory. 650 0 Mathematics |xHistory. 653 Benedetto. 653 Black-Scholes formula. 653 Eugene Wigner. 653 Friedrich W.J. Schelling. 653 George Lakoff. 653 Gilles Deleuze. 653 Hermann Cohen. 653 Hilary Putnam. 653 Johann G. Fichte. 653 Logic of Sensation. 653 Mark Steiner. 653 Rafael Nez. 653 Stanislas Dehaene. 653 Vincent Walsh. 653 Water J. Freeman III. 653 abbaco. 653 algebra. 653 arithmetic. 653 authority. 653 cognitive theory. 653 combinatorics. 653 conceptual freedom. 653 constraints. 653 economy. 653 gender role stereotypes. 653 generating functions. 653 geometry. 653 inferences. 653 infinities. 653 infinity. 653 mathematical cognition. 653 mathematical concepts. 653 mathematical cultures. 653 mathematical domains. 653 mathematical entities. 653 mathematical evolution. 653 mathematical interpretation. 653 mathematical language. 653 mathematical metaphor. 653 mathematical norms. 653 mathematical objects. 653 mathematical practice. 653 mathematical signs. 653 mathematical standards. 653 mathematical statements. 653 mathematics. 653 natural order. 653 natural sciences. 653 nature. 653 negative numbers. 653 number sense. 653 option pricing. 653 philosophy of mathematics. 653 reality. 653 reason. 653 relevance. 653 semiosis. 653 sexuality. 653 stable marriage problem. 655 4 History 655 4 Electronic books. 776 |z0-691-17171-8 776 |z1-4008-8378-4 906 BOOK