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The last big things that we discovered was the constructivist turn in mathematics... to understand that the parts of mathematics that work are computation. That was a very significant discovery in the first half of the 20th century. ...t hasn't fully permeated philosophy and even physics yet. Physicists checked out the code libraries for mathematics before constructivism became universal. ...Gödel himself ...didn't get it yet. Hilbert could get it. Hilbert saw that Cantor's set theoretic experiments in mathematics led him to contradictions, and he noticed that with the current semantics we cannot build a computer in mathematics that runs mathematics without crashing, and Gödel... could prove this. (en) |
