GEB not just a popular exposition of mathematical logic, the book is quite explicitly about philosophy of mind. In particular, he develops the self-reference stuff so he can draw an analogy to brains and tell us his theory of consciousness. As for support for that claim, he clarified the point of the book in an elaborate preface to the 20th anniversary edition, and that still wasn't enough to get the point across, so he wrote an entire second book ('I am a Strange Loop') to explain his theory of mind again.
Exactly. Godel's Incompleteness Theorems have as much to do with philosophy of mind (consciousness/brains/AI) as the Pythagorean Theorem does.
I found I Am a Strange Loop good, but a little sad.
How is that a "misuse" of Godel's Theorem? He doesn't draw conclusions from it about consciousness. He only points to it as an example of a strange loop. Godel's Theorem is an analogy, not an explanation.
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.
Re:Gödel's Theorem
by googlemike on Thursday January 31, 2019 @01:45AM
(#19042928)
+1
It is odd to think of someone "using" or "misusing" Godel - if the points are salient and clear, how is it misuse? (At least, in this case, where GEB is a philosophical text, not a scientific one.)
Assuming this is Hofstader's Godel Escher Bach, I'd like to see support for this claim. GEB is just a popular exposition of Godel and a paean to self-reference. It's not a rigorous work but I don't know of any terrible violations it involves.