{"product_id":"making-and-breaking-mathematical-sense-9780691171715","title":"Making and Breaking Mathematical Sense","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"[Making and Breaking Mathematical Sense] offers a substantial and interesting treatment of issues in the philosophy of mathematical practice.\"--Calvin Jongsma, MAA Reviews\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eAcknowledgments xi  Introduction 1  What Philosophy of Mathematics Is Today 1  What Else Philosophy of Mathematics Can Be 3  A Vignette: Option Pricing and the Black-Scholes Formula 6  Outline of This Book 10  1: Histories of Philosophies of Mathematics 13  History 1: On What There Is, Which Is a Tension between Natural Order and Conceptual Freedom 14  History 2: The Kantian Matrix, Which Grants Mathematics a Constitutive Intermediary Epistemological Position 22  History 3: Monster Barring, Monster Taming, and Living with Mathematical Monsters 28  History 4: Authority, or Who Gets to Decide What Mathematics Is About 33  The \"Yes, Please!\" Philosophy of Mathematics 37  2: The New Entities of Abbacus and  Renaissance Algebra 39  Abbacus and Renaissance Algebraists 39  The Emergence of the Sign of the Unknown 40  First Intermediary Reflection 45  The Arithmetic of Debited Values 46  Second Intermediary Reflection 51  False and Sophistic Entities 53  Final Reflection and Conclusion 56  3: A Constraints-Based Philosophy of Mathematical Practice 59  Dismotivation 59  The Analytic A Posteriori 63  Consensus 67  Interpretation 72  Reality 81  Constraints 84  Relevance 90  Conclusion 97  4: Two Case Studies of Semiosis in Mathematics 100  Ambiguous Variables in Generating Functions 101  Between Formal Interpretations 101  Models and Applications 107  Openness to Interpretation 109  Gendered Signs in a Combinatorial Problem 112  The Problem 112  Gender Role Stereotypes and Mathematical Results 116  Mathematical Language and Its Reality 120  The Forking Paths of Mathematical Language 122  5: Mathematics and Cognition 128  The Number Sense 129  Mathematical Metaphors 137  Some Challenges to the Theory of Mathematical Metaphors 142  Best Fit for Whom? 143  What Is a Conceptual Domain? 146  In Which Direction Does the Theory Go? 150  So How Should We Think about Mathematical Metaphors? 154  An Alternative Neural Picture 156  Another Vision of Mathematical Cognition 163  From Diagrams to Haptic Vision 164  Haptic Vision in Practice 171  6: Mathematical Metaphors Gone Wild 177  What Passes between Algebra and Geometry 177  Piero della Francesca (Italy, Fifteenth Century) 178  Omar Khayyam (Central Asia, Eleventh Century) 179  Rene Descartes (France, Seventeenth Century) 181  Rafael Bombelli (Italy, Sixteenth Century) 183  Conclusion 187  A Garden of Infinities 188  Limits 189  Infinitesimals and Actual Infinities 194  7: Making a World, Mathematically 199  Fichte 201  Schelling 206  Hermann Cohen 209  The Unreasonable(?) Applicability of Mathematics 213  Bibliography 219  Index 233","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403830042967,"sku":"9780691171715","price":999.99,"currency_code":"GBP","in_stock":false}],"url":"https:\/\/bookcurl.com\/products\/making-and-breaking-mathematical-sense-9780691171715","provider":"Book Curl","version":"1.0","type":"link"}