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

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Basic Books, 2000 - Mathematics - 493 pages
17 Reviews
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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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 ... Read full review

Review: Where Mathematics Come From: How the Embodied Mind Brings Mathematics into Being

User Review  - Joseph - Goodreads

Lakoff and Nunez are cognitive scientists with a deep interest in mathematics and in this book, they try to explain mathematics from a cognitive perspective. The result is fascinating. I am a ... Read full review

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
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

Real Numbers and Limits
181
Transfinite Numbers
208
Infinitesimals
223
Points and the Continuum
259
Case Study 4 e𝝅𝙞 + 1 0 How the Fundamental Ideas of Classical Mathematics Fit Together
433
References
453
Index
473
Copyright

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About the author (2000)

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.

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