Sigh. Maybe you'll be offended by me saying this, but often when someone makes statements like this I have to wonder if they're just being coy. [edit] After all, you shrug and say there's no paradox when that very article says no answer is yet universally accepted.
Hofstadter's book is a bit difficult to classify. By profession AI is his thing. So, he talks about the difficulties of coding information and wonders how humans manage to store so much. He talks about the mechanisms of the brain and how little they are understood - which is where the grandma cell comes in. Even if it is not a literal mechanism, it serves as a challenge to AI and neuroscience that has not yet been met - to explain the connection between senses, perception, storage, and recall. He also talks about determinism vs. freedom and the logical difficulties this creates as one is led into an infinite regress. As I've described the book you may think he is skeptical of what AI and neuroscience can achieve. Not so. He is a devout optimist about it all. He thinks he has answers to many of those puzzles, and expects answers to be found for the unsolved ones. The conclusion is mine that, for the length of the book, and as fascinating as it is, in the end he demonstrates very little.
So, I'm at a loss to understand what you don't get. If you think neuroscience is, in its present state, fully capable of demonstrating all aspects of "mind" that were once claimed to be metaphysical, then I suppose it is I who should be asking you questions. I just read a recent PhD that said we're not there yet, and I assumed someone studying in the field would have a better handle on it than me, but maybe there is a source disputing that claim of which I'm unaware.
Starting from the example of intelligence, then, do you have a reference that explains the physical construct that produces intelligence? I'm not talking about knowing wherecertain centers of the brain are, or knowing how to shut off certain behaviors with specific chemical blockers, or even knowing what treatments assist people with certain conditions. And I'll allow putting aside manufacturing issues, i.e. that we can't build our own neurons yet. I mean, does someone have a model of the brain such that, if it were possible to build that model, it would exhibit intelligence in a manner comparable to the human mind? Not just that it would win a chess game, but that it would grasp all aspects of human intelligence?