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Synopsis
Provides an in-depth analysis of the cognitive science of mathematical ideas that argues that conceptual metaphor plays a definitive role in mathematical ideas, exploring such concepts as arithmetic, algebra, sets, logic, and infinity.
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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.
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Where Mathematics Come From : How the Embodied Mind Brings Mathematics into Being
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