That's not at all an accurate description of the book. Goedel is not just used as an example of a strange loop, he bases his entire model of mind on it. This is

That's not at all an accurate description of the book. Goedel is not just used as an example of a strange loop, he bases his entire model of mind on it. This is developed in chapter 20. Particularly noteworthy are the sections of that chapter titled "Undecidability is inseparable from a high-level viewpoint", immediately followed by "consciousness as an intrinsically high-level phenomenon". It's true that he uses it as an analogy, but not a loose or vague one. For example, "But it is important to realize that if we are being guided by Goedel's proof in making such bold hypotheses, we must carry the analogy through thoroughly [...] If our analogy is to hold, then, 'emergent' phenomena would become explicable in terms of a relationship between different levels in mental systems." p708 He's literally taking the logic of Goedel's proof, transferring it to brains step by step, to argue for a particular theory of consciousness.