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/...
Don't discount metaphors -- they're a critical part of everyday communication because our conceptual system is largely metaphorical. We think in metaphors. They're the concepts we live by. They're the abstractions that help us relate and understand.
For an in-depth perspective, read George Lakoff and Mark Johnson's classic "Metaphors We Live By" (http://www.amazon.com/Metaphors-We-Live-George-Lakoff/dp/022...). Here's Peter Norvig's review of it: http://norvig.com/mwlb.html .
[0] https://www.amazon.com/Metaphors-We-Live-George-Lakoff/dp/02...