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

• Autore: Wagner Roi
• Pubblicazione: Princeton, NJ : , : Princeton University Press, , [2017]; ©2017
• Descrizione fisica: 1 online resource (251 pages)
• Disciplina: 510.1
• Soggetto topico: Mathematics - Philosophy - History; Mathematics - History
• Soggetto genere / forma: History; Electronic books.
• Soggetto non controllato: Benedetto; Black-Scholes formula; Eugene Wigner; Friedrich W.J. Schelling; George Lakoff; Gilles Deleuze; Hermann Cohen; Hilary Putnam; Johann G. Fichte; Logic of Sensation; Mark Steiner; Rafael Nez; Stanislas Dehaene; Vincent Walsh; Water J. Freeman III; abbaco; algebra; arithmetic; authority; cognitive theory; combinatorics; conceptual freedom; constraints; economy; gender role stereotypes; generating functions; geometry; inferences; infinities; infinity; mathematical cognition; mathematical concepts; mathematical cultures; mathematical domains; mathematical entities; mathematical evolution; mathematical interpretation; mathematical language; mathematical metaphor; mathematical norms; mathematical objects; mathematical practice; mathematical signs; mathematical standards; mathematical statements; mathematics; natural order; natural sciences; nature; negative numbers; number sense; option pricing; philosophy of mathematics; reality; reason; relevance; semiosis; sexuality; stable marriage problem
• Note generali: Previously issued in print: 2017.
• Nota di bibliografia: Includes bibliographical references (pages 219-231) and index.
• Nota di contenuto: 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. ; 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. ; 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? ; 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. ; SchellingHermann Cohen; The Unreasonable Applicability of Mathematics; Bibliography; Index.
• Sommario/riassunto: 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.
• Titolo autorizzato: Making and Breaking Mathematical Sense
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910154298703321
• Lo trovi qui: Univ. Federico II