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基本説明
New in paperback. Hardcover was published in 2000.
邦訳:2012年12月・丸善出版。
Full Description
This book is about mathematical ideas, about what mathematics means-and why. Abstract ideas, for the most part, arise via conceptual metaphor-metaphorical ideas projecting from the way we function in the everyday physical world. Where Mathematics Comes From argues that conceptual metaphor plays a central role in mathematical ideas within the cognitive unconscious-from arithmetic and algebra to sets and logic to infinity in all of its forms.
Table of Contents
Acknowledgments ix
Preface xi
Introduction: Why Cognitive Science Matters to 1 (14)
Mathematics
Part I THE EMBODIMENT OF BASIC ARITHMETIC
The Brain's Innate Arithmetic 15 (12)
A Brief Introduction to the Cognitive Science 27 (23)
of the Embodied Mind
Embodied Arithmetic: The Grounding Metaphors 50 (27)
Where Do the Laws of Arithmetic Come From? 77 (30)
Part II ALGEBRA, LOGIC, AND SETS
Essence and Algebra 107(14)
Boole's Metaphor: Classes and Symbolic Logic 121(19)
Sets and Hypersets 140(15)
Part III THE EMBODIMENT OF INFINITY
The Basic Metaphor of Infinity 155(26)
Real Numbers and Limits 181(27)
Transfinite Numbers 208(15)
Infinitesimals 223(36)
Part IV BANNING SPACE AND MOTION: THE
DISCRETIZATION PROGRAM THAT SHAPED MODERN
MATHEMATICS
Points and the Continuum 259(33)
Continuity for Numbers: The Triumph of 292(14)
Dedekind's Metaphors
Calculus Without Space or Motion: 306(31)
Weierstrass's Metaphorical Masterpiece
Le trou normand: A Classic Paradox of 325(12)
Infinity
Part V IMPLICATIONS FOR THE PHILOSOPHY OF
MATHEMATICS
The Theory of Embodied Mathematics 337(27)
The Philosophy of Embodied Mathematics 364(89)
Part VI eπi + 1 = 0 A CASE STUDY OF THE
COGNITIVE STRUCTURE OF CLASSICAL MATHEMATICS
Analytic Geometry and Trigonometry 383(16)
What Is e? 399(21)
What Is i? 420(13)
eπi + 1 = 0--How the Fundamental Ideas 433(20)
of Classical Mathematics Fit Together
References 453(20)
Index 473