LEADER 07764nam 22012855 450 001 9910154298703321 005 20240708094202.0 024 7 $a10.1515/9781400883783 035 $a(CKB)3710000000918032 035 $a(MiAaPQ)EBC4778017 035 $a(StDuBDS)EDZ0001815924 035 $a(DE-B1597)479741 035 $a(OCoLC)968732589 035 $a(OCoLC)984687424 035 $a(DE-B1597)9781400883783 035 $a(MdBmJHUP)musev2_125632 035 $a(EXLCZ)993710000000918032 100 $a20190523d2017 fg 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aMaking and Breaking Mathematical Sense $eHistories and Philosophies of Mathematical Practice /$fRoi Wagner 210 1$aPrinceton, NJ :$cPrinceton University Press,$d[2017] 210 4$dİ2017 215 $a1 online resource (251 pages) 300 $aPreviously issued in print: 2017. 311 $a0-691-17171-8 311 $a1-4008-8378-4 320 $aIncludes bibliographical references (pages 219-231) and index. 327 $aCover; 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. 327 $aHistory 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. 327 $aChapter 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? 327 $aSo 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. 327 $aSchellingHermann Cohen; The Unreasonable Applicability of Mathematics; Bibliography; Index. 330 $aIn 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. 606 $aMathematics$xPhilosophy$xHistory 606 $aMathematics$xHistory 608 $aHistory 608 $aElectronic books. 610 $aBenedetto. 610 $aBlack-Scholes formula. 610 $aEugene Wigner. 610 $aFriedrich W.J. Schelling. 610 $aGeorge Lakoff. 610 $aGilles Deleuze. 610 $aHermann Cohen. 610 $aHilary Putnam. 610 $aJohann G. Fichte. 610 $aLogic of Sensation. 610 $aMark Steiner. 610 $aRafael Nez. 610 $aStanislas Dehaene. 610 $aVincent Walsh. 610 $aWater J. Freeman III. 610 $aabbaco. 610 $aalgebra. 610 $aarithmetic. 610 $aauthority. 610 $acognitive theory. 610 $acombinatorics. 610 $aconceptual freedom. 610 $aconstraints. 610 $aeconomy. 610 $agender role stereotypes. 610 $agenerating functions. 610 $ageometry. 610 $ainferences. 610 $ainfinities. 610 $ainfinity. 610 $amathematical cognition. 610 $amathematical concepts. 610 $amathematical cultures. 610 $amathematical domains. 610 $amathematical entities. 610 $amathematical evolution. 610 $amathematical interpretation. 610 $amathematical language. 610 $amathematical metaphor. 610 $amathematical norms. 610 $amathematical objects. 610 $amathematical practice. 610 $amathematical signs. 610 $amathematical standards. 610 $amathematical statements. 610 $amathematics. 610 $anatural order. 610 $anatural sciences. 610 $anature. 610 $anegative numbers. 610 $anumber sense. 610 $aoption pricing. 610 $aphilosophy of mathematics. 610 $areality. 610 $areason. 610 $arelevance. 610 $asemiosis. 610 $asexuality. 610 $astable marriage problem. 615 0$aMathematics$xPhilosophy$xHistory. 615 0$aMathematics$xHistory. 676 $a510.1 700 $aWagner$b Roi$01224460 801 0$bDE-B1597 801 1$bDE-B1597 906 $aBOOK 912 $a9910154298703321 996 $aMaking and Breaking Mathematical Sense$92842225 997 $aUNINA