Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being,9780465037711

Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being

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Edition: Reprint
ISBN13: 9780465037711
ISBN10: 0465037712
Format: Paperback
Pub. Date: 2001-08-16
Publisher(s): Basic Books
List Price: $34.23

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Summary

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.

Author Biography

George Lakoff is Professor of Linguistics at the University of California, Berkeley. He was a founder of the generative semantics movements in linguistics in the 1960s and of the field of cognitive linguistics in the 1970s, and one of the developers of the neural theory of language in the 1980s and '90s. He is the co-author, with Mark Johnson, of Metaphors We Live By and Philosophy in the Flesh.Rafael Nuñez is currently at the Department of Psychology of the University of Freiburg, and is a research associate of the University of California, Berkeley. He is the co-editor of Reclaiming Cognition: The Primacy of Action, Intention and Emotion.

Table of Contents

Acknowledgments ix
Preface xi
Introduction: Why Cognitive Science Matters to Mathematics 1(14)
Part I THE EMBODIMENT OF BASIC ARITHMETIC
The Brain's Innate Arithmetic
15(12)
A Brief Introduction to the Cognitive Science of the Embodied Mind
27(23)
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 Dedekind's Metaphors
292(14)
Calculus Without Space or Motion: Weierstrass's Metaphorical Masterpiece
306(31)
Le trou normand: A Classic Paradox of Infinity
325(12)
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 of Classical Mathematics Fit Together
433(20)
References 453(20)
Index 473

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