Douglas Hofstadter is a larger-than-life academic researcher who manages to combine a thirst for beautiful forms with the most penetrating theoretical insights, whether it is in mathematics, music, linguistics, philosophy, or the visual arts. He is a Professor of Cognitive Sciences but also has an involvement in Philosophy, Comparative Literature, Psychology...
No surprise then that he gravitates to the most fundamental overlapping problems, the notion of the self, the I, the problems of volition, perception, mind, and consciousness. These problems are notoriously difficult to understand because we are the object of our own study. They involve thinking deeply about perception and its mechanisms, about symbols in our brains and how they might affect our actions, about how we can conceive of our mind as being separate from the reality we are part of, and about how all of this can develop in a human being.
But Hofstadter is no typical academic author. Instead of writing a theoretical tome, he has written a highly entertaining and challenging book using a mixture of descriptions, anecdotes, dialogues, photographs and visual illustrations, and weaves in fundamental arguments in philosophy, mathematics, neuroscience, language, and a host of other areas. Because he relies on many concrete examples and illustrations, the reader does not need expertise in any of these subjects and the work, though challenging, is very accessible.
Hofstadter draws on the work of Kurt Gödel, an Austrian mathematician and logician, who in 1931 showed that a consistent arithmetic based on axioms can contain true propositions that can't be proved by those axioms alone. That seemingly yawn-inducing result was so significant that it changed the way we think about mathematics and logic forever. Gödel was describing a mechanism of self-reference.
But there's a problem with self-reference — infinite regress. So, for example, if you think about yourself thinking about yourself thinking about yourself... there's no end point. Gödel though, showed it was possible to provide a self-referential process which didn't have that problem of infinite regress. He did it by turning theorems about numbers into numbers themselves, but we don't need to go into the abstruse details.
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