Where Mathematics Come From: How The Embodied Mind Brings Mathematics Into Being
by
George Lakoff
Description: Where Mathematics Come From: How The Embodied Mind Brings Mathematics Into Being examines the origins of mathematical concepts through the lens of cognitive science, focusing on how human thought shapes mathematical understanding and meaning
ISBN: 0465037712
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If you want to understand Godel's proofs then I recommend the book "Godel's Proof" by Ernest Nagel and James R. Newman:
http://www.amazon.com/Gödels-Proof-Ernest-Nagel/dp/081475837...
Instead of Hofstadter's GEB, read some of his papers, e.g., "Analogy as the Core of Cognition" http://prelectur.stanford.edu/lecturers/hofstadter/analogy.h...
But there are others who have focused longer on analogy, e.g., George Lakoff:
"Metaphors we Live by"
http://www.amazon.com/Metaphors-We-Live-George-Lakoff/dp/022...
"Where Mathematics Come From: How The Embodied Mind Brings Mathematics Into Being":
http://www.amazon.com/Where-Mathematics-Come-Embodied-Brings...
"Women, Fire, and Dangerous Things"
http://www.amazon.com/Women-Fire-Dangerous-Things-Lakoff/dp/...