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

Front Cover
Basic Books, Nov 2, 2000 - Mathematics - 493 pages
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.

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User Review  - johnverdon - LibraryThing

George Lakoff is a national treasure - who through is career and many collaborations has provided that evidence of the inevitability and importance of metaphor. Metaphor structures how we reason - via ... Read full review

LibraryThing Review

User Review  - mykl-s - LibraryThing

Interesting follow-up to Lakoff's Metaphors We Live By. The thesis here is that all language is metaphorical expression, which is based on conceptual metaphors determined by the brain as well as by ... Read full review

Contents

Why Cognitive Science Matters to Mathematics 1
1
The Brains Innate Arithmetic
15
A Brief Introduction to the Cognitive Science of the Embodied Mind
27
Copyright

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