Doug Hofstadter: Reflections on AI
Getting2Alpha
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Gödel's Recursion
Girdle: The self-reference in Gödel's construction comes about in a way that is very surprising. In 19 roughly 10 to 13 Bertrand Russell and Alfred North Whitehead, two important philosophers created a work called Principia Mathematica meaning the bases of mathematics. And so he could create a sentence that was about numbers, but at the same time it could be read at a second level so that it was about symbols. He wound up finding, creating a self-referential sentence in the fortress that Bertrand Russell had erected to banish self-reference from. It turned self-reference into something that was inevitable, even despite the best efforts to banish it.
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