https://en.wikipedia.org/wiki/To_Mock_a_Mockingbird
Smullyan "tricks" you into deriving the Gödel Incompleteness Theorem from the BCKW combinator calculus.
[1] https://www.amazon.com/Gödels-Proof-Ernest-Nagel/dp/08147583...
Both books are ultimately focused on the nature of consciousness, although from quite different perspectives. In both cases, the theorem is presented as one element of an argument.
It's interesting that two sophisticated writers with wildly different opinions about consciousness have both leaned on Gödel to back their arguments. There's nothing in the theorem that shouts "This is about consciousness!"
https://en.m.wikipedia.org/wiki/Penrose–Lucas_argument
Thanks for answering my question. I am guessing that neither book would explaim the proof in detail.
I understand the idea of Gödel numbering; I understand Cantor's diagonal slash; but I struggle to assemble the components into a proof that convinces me. I think I just lack the cerebral capacity.