Where Mathematics Come from: How the Embodied Mind Brings Mathematics into Being

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Overview

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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More About This Book

Overview

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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Editorial Reviews

American Scholar
Adds body heat to the cold and beautiful abstractions of mathematics.
Science News
. . .[a] groundbreaking book. . .
Science News
A groundbreaking book.
Publishers Weekly - Publisher's Weekly
This groundbreaking exploration by linguist Lakoff (co-author, with Mark Johnson, of Metaphors We Live By) and psychologist N ez (co-editor of Reclaiming Cognition) brings two decades of insights from cognitive science to bear on the nature of human mathematical thought, beginning with the basic, pre-verbal ability to do simple arithmetic on quantities of four or less, and encompassing set theory, multiple forms of infinity and the demystification of more enigmatic mathematical truths. Their purpose is to begin laying the foundations for a truly scientific understanding of human mathematical thought, grounded in processes common to all human cognition. They find that four distinct but related processes metaphorically structure basic arithmetic: object collection, object construction, using a measuring stick and moving along a path. By carefully unfolding these primitive examples and then building upon them, the authors take readers on a dazzling excursion without sacrificing the rigor of their exposition. Lakoff and N ez directly challenge the most cherished myths about the nature of mathematical truth, offering instead a fresh, profound, empirically grounded insight into the meaning of mathematical ideas. This revolutionary account is bound to garner major attention in the scientific press--but it remains a very challenging read that lends itself mostly to those with a strong interest in either math or cognitive science. (Nov. 15) Copyright 2000 Cahners Business Information.
Booknews
Two cognitive scientists examine the structure of mathematical ideas, what mathematics means, and why. Lakoff (linguistics, U. of California, Berkeley) and N<'u><~n>ez (psychology, U. of Freiburg) believe that conceptual metaphor plays a central, defining role in mathematical ideas, from simple arithmetic and algebra to sets, logic, and infinity. They argue that understanding the ideas implicit in mathematics, especially the metaphorical ideas, demystifies mathematics so that it makes more sense. Annotation c. Book News, Inc., Portland, OR (booknews.com)
From The Critics
The only math ideas humans can have are ideas invented by the human brain: Where Mathematics Comes From argues that a conceptual metaphor plays a defining role in math ideas within the unconscious, drawing important connections between mathematical ideas and what they mean. It's the first serious study of the cognitive science of where math ideas originate: college-level audiences will find it involving.
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Product Details

  • ISBN-13: 9780465037711
  • Publisher: Basic Books
  • Publication date: 8/14/2001
  • Edition description: Reprint
  • Pages: 492
  • Sales rank: 437,212
  • Product dimensions: 7.41 (w) x 9.22 (h) x 1.12 (d)

Meet 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.

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