Where Mathematics Come From

How The Embodied Mind Brings Mathematics Into Being

By: George Lakoff, Rafael Nunez

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Paperback | 16 August 2001 | Edition Number 1

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512 Pages

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Renowned linguist George Lakoff pairs with psychologist Rafael Nuez in the first book to provide a serious study of the cognitive science of mathematical ideas.. 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.

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You Can Find This Book In

Non-Fiction Psychology Cognition & Cognitive Psychology Miscellaneous Items Mathematics Philosophy of Mathematics Science Science in General History of Mathematics Number Theory

Acknowledgments	p. ix
Preface	p. xi
Introduction: Why Cognitive Science Matters to Mathematics	p. 1
The Embodiment of Basic Arithmetic
The Brain's Innate Arithmetic	p. 15
A Brief Introduction to the Cognitive Science of the Embodied Mind	p. 27
Embodied Arithmetic: The Grounding Metaphors	p. 50
Where Do the Laws of Arithmetic Come From?	p. 77
Algebra, Logic, and Sets
Essence and Algebra	p. 107
Boole's Metaphor: Classes and Symbolic Logic	p. 121
Sets and Hypersets	p. 140
The Embodiment of Infinity
The Basic Metaphor of Infinity	p. 155
Real Numbers and Limits	p. 181
Transfinite Numbers	p. 208
Infinitesimals	p. 223
Banning Space and Motion: The Discretization Program That Shaped Modern Mathematics
Points and the Continuum	p. 259
Continuity for Numbers: The Triumph of Dedekind's Metaphors	p. 292
Calculus Without Space or Motion: Weierstrass's Metaphorical Masterpiece	p. 306
Le trou normand: A Classic Paradox of Infinity	p. 325
Implications for the Philosophy of Mathematics
The Theory of Embodied Mathematics	p. 337
The Philosophy of Embodied Mathematics	p. 364
e[superscript pi i] + 1 = 0 A Case Study of the Cognitive Structure of Classical Mathematics
Analytic Geometry and Trigonometry	p. 383
What Is e?	p. 399
What Is i?	p. 420
e[superscript pi i] + 1 = 0--How the Fundamental Ideas of Classical Mathematics Fit Together	p. 433
References	p. 453
Index	p. 473
Table of Contents provided by Syndetics. All Rights Reserved.

Where Mathematics Come From

How The Embodied Mind Brings Mathematics Into Being

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Paperback

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