I already knew about Godel’s theorem before reading this book, and its consequences about the unknownability is what I had focused on. I find it fascinating how one can sometime build extended models by changing small aspects of the founding axioms (for example, how one can get non-standard models with transfinite numbers, and use them to build infinitesimals by simply assuming that there are numbers that are not reached by a proof by induction starting at 0 (I did a course on that).
Douglas R. Hofstadter is different, the unasking, the MU answer to paradox can be seen as an extension of what I was thinking, but then he goes beyond that, he looks in particular at the self referentiality and its consequences, and how this can relate to consciousness, and how this question also comes up and is treated in Art, in particular Escher and Bach’s
On the whole a fascinating book, that I can highly recommend, but probably quite heavy for someone not so passionate about logic.
After reading the book I followed a course on the “Papillon d’Hofstadter”: the fractal structure of the spectrum of an operator coming from the interaction of electrons in a periodic potential. The seminar was very interesting, I also followed it because I had read the book. It isn’t directly related to the themes of the book, but the fractal structure might have inspired some themes. I got to know better bounded operators, and it was nice to get to know another facet that I did not expect of Douglas R. Hofstadter.
Writing this review I saw that there are new books, Metamagical themas: questing the essence of mind and pattern (a collection of articles published in Scientific American), but especially I am a strange loop, time to hit the library…