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

Lakoff, George; Nunez, Rafael

 
9780465037704: Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being
Hardcover
ISBN 10: 0465037704 ISBN 13: 9780465037704
Publisher: Basic Books, 2000

Synopsis

When you think about it, it seems obvious: The only mathematical ideas that human beings can have are ideas that the human brain allows. We know a lot about what human ideas are like from research in Cognitive Science. Most ideas are unconscious, and that is no less true of the mathematical ones. Abstract ideas, for the most part, arise via conceptual metaphor-a mechanism for projecting embodied (that is, sensory-motor) reasoning to abstract reasoning. This book argues that conceptual metaphor plays a central, defining role in mathematical ideas within the cognitive unconscious-from arithmetic and algebra to sets and logic to infinity in all of its forms: transfinite numbers, points at infinity, infinitesimals, and so on. Even the real numbers, the imaginary numbers, trigonometry, and calculus are based on metaphorical ideas coming out of the way we function in the everyday physical world.This book is about mathematical ideas, about what mathematics means-and why. The authors believe that understanding the metaphors implicit in mathematics will make mathematics make more sense. Moreover, understanding mathematical ideas and how they arise from our bodies and brains will make it clear that the brain's mathematics is mathematics, the only mathematics we know or can know.

"synopsis" may belong to another edition of this title.

Synopsis

Linguist George Lakoff pairs with psychologist Rafael Nuez in the first book to provide a serious study of the cognitive science of mathematical ideas. When you think about it, it seems obvious: the only mathematical ideas that human beings can have are ideas that the human brain allows. We know a lot about what human ideas are like from research in cognitive science. Most ideas are unconscious, and that is no less true of the mathematical ones. Abstract ideas, for the most part, arise via conceptual metaphor - a mechanism for projecting embodied (that is, sensory-motor) reasoning to abstract reasoning. This book argues that conceptual metaphor plays a central, defining role in mathematical ideas within the cognitive unconscious - from arithmetic and algebra to sets and logic to infinity in all of its forms: transfinite numbers, points at infinity, infinitesimals, and so on. Even the real numbers, the imaginary numbers, trigonometry, and calculus are based on metaphorical ideas coming out of the way we function in the everyday physical world.

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.

"About this title" may belong to another edition of this title.

Publisher
Basic Books
Publication date
2000
Language
English
ISBN 10 
0465037704
ISBN 13 
9780465037704
Binding
Hardcover
Edition number
1
Number of pages
512