Mathematical Knowledge and the Interplay of Practices

Synopsis

This Book Presents A New Approach To The Epistemology Of Mathematics By Viewing Mathematics As A Human Activity Whose Knowledge Is Intimately Linked With Practice. Charing An Exciting New Direction In The Philosophy Of Mathematics. José Ferreirós Uses The Crucial Idea Of A Continuum To Provide An Account Of The Development Of Mathematical Knowledge That Reflects The Actual Experience Of Doing Math And Makes Sense Of The Perceived Objectivity Of Mathematical Results. Describing A Historically Oriented, Agent-based Philosophy Of Mathematics, Ferreirós Shows How The Mathematical Tradition Evolved From Euclidean Geometry To The Real Numbers And Set-theoretic Structures. He Argues For The Need To Take Into Account A Whole Web Of Mathematical And Other Practices That Are Learned And Linked By Agents, And Whose Interplay Acts As A Constraint. Ferreirós Demonstrates How Advanced Mathematics, Far From Being A Priori, Is Based On Hypotheses, In Contrast To Elementary Math, Which Has Strong Cognitive And Practical Roots And Therefore Enjoys Certainty. Offering A Wealth Of Philosophical And Historical Insights, Mathematical Knowledge And The Interplay Of Practices Challenges Us To Rethink Some Of Our Most Basic Assumptions About Mathematics, Its Objectivity, And Its Relationship To Culture And Science. -- From Back Cover. On Knowledge And Practices: A Manifesto -- The Web Of Practices -- Agents And Frameworks -- Complementarity In Mathematics -- Ancient Greek Mathematics: A Role For Diagrams -- Advanced Math: The Hypothetical Conception -- Arithmetic Certainty -- Mathematics Developed: The Case Of The Reals -- Objectivity In Mathematical Knowledge -- The Problem Of Conceptual Understanding José Ferreirós. Includes Bibliographical References (pages 315-330) And Index.