[annie511266728]

Yeah, I think that's the tradeoff.

Löb gets you to the main idea faster, but Gödel numbering is the part that makes it feel like the system is actually doing it itself.

Without that step, it can start to feel a bit too close to the liar paradox.

[cousin_it]

Yeah. I'd say half of the work is Gödel numbering and the other half is the diagonal lemma.

[mjh2539]

This is the most apt answer I've read thus far.