It's been years since I cracked open a copy, maybe I should give it another shot.
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If you want to get to the meat of the issue, without the extraneous stuff, you might also tackle: Godel's Theorem Simplified.
https://www.amazon.com/Godels-Theorem-Simplified-Harry-Gensl...
The extraneous stuff is honestly fabulous, IMO of course. Just being able to listen to a four part fugue sensibly is a rare but accessible pleasure. And amusing dialogs as an instantiated dialectic for showing the truth synthesized from apparent opposites, is a great pedagogical learning.
Extremely agree. The extraneous stuff is what makes the book magical.