Front cover image for Where mathematics comes from : how the embodied mind brings mathematics into being

Where mathematics comes from : how the embodied mind brings mathematics into being

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. -- Publisher description
Print Book, English, ©2000
Basic Books, New York, NY, ©2000
xvii, 492 pages : illustrations ; 25 cm
9780465037704, 9780465037711, 0465037704, 0465037712
The embodiment of basic arithmetic
Algebra, logic, and sets
The embodiment of infinity
Banning space and motion : the discretization program that shaped modern mathematics
Le trou normand : A classic paradox of infinity
Implications for the philosophy of mathematics
A case study of the cognitive structure of classical mathematics Donated in memory of William John Patterson