Where Mathematics Comes from: How the Embodied Mind Brings Mathematics Into Being

George Lakoff, Rafael E. Núñez

Basic Books, 2000 - Mathematics - 493 pages

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.

What people are saying

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

User Review  - Carrie - Goodreads

I find some of the arguments in this book tautological, thought it is difficult to articulate why. The section on an Embodied Philosophy of Mathematics is one of the most interesting in the book. The ...

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

User Review  - Joe - Goodreads

A superbly written mathematics book for geeks and non-geeks alike. OK it's better if you're a little geeky. The author is a linquist, and provides compelling metaphorical explanations for difficult ...

Contents

• The Brains Innate Arithmetic: 15
• A Brief Introduction to the Cognitive Science of the Embodied Mind: 27
• Embodied Arithmetic The Grounding Metaphors: 50
• Where Do the Laws of Arithmetic Come From?: 77
• Essence and Algebra: 107
• Booles Metaphor Classes and Symbolic Logic: 121
• Sets and Hypersets: 140
• The Basic Metaphor of Infinity: 155
• Real Numbers and Limits: 181
• Transfinite Numbers: 208
• Infinitesimals: 223
• Points and the Continuum: 259
• Continuity for Numbers The Triumph of Dedekinds Metaphors: 292
• Calculus Without Space or Motion Weierstrasss Metaphorical Masterpiece: 306
• A Classic Paradox of Infinity: 325
• The Theory of Embodied Mathematics: 337
• The Philosophy of Embodied Mathematics: 364
• Case Study 1 Analytic Geometry and Trigonometry: 383
• Case Study 2 What Is e?: 399
• Case Study 3 What Is i?: 420
• Case Study 4 e𝝅𝙞 + 1 0 How the Fundamental Ideas of Classical Mathematics Fit Together: 433
• References: 453
• Index: 473

About the author

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.

Bibliographic information

• Title: Where Mathematics Comes from: How the Embodied Mind Brings Mathematics Into Being
• Authors: George Lakoff, Rafael E. Núñez
• Edition: illustrated, reprint
• Publisher: Basic Books, 2000
• ISBN: 0465037712, 9780465037711
• Length: 493 pages
• Subjects: Mathematics / General; Mathematics / History & Philosophy; Psychology / Cognitive Psychology