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“In particular, what our minds could not be, so goes the reasoning, are computers. The mathematical knowledge that we possess cannot be captured in a formal system. That is what Gödel's first incompleteness theorem seems to tell us. But formal systems are precisely what captures the computing of computers, which is why they are able to figure things out without having any recourse to meanings. Computers run according to algorithms and we, it seems, do not, from which straightforwardly follows that our minds are not computers.”
-- Rebecca Goldstein
