Sebastian_Hagen comments on The Amanda Knox Test: How an Hour on the Internet Beats a Year in the Courtroom - Less Wrong
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That's incorrect. As shown by Gödel's second incompleteness theorem, mathematical formal systems divide into three categories:
When doing math, humans tend to assume that certain formal systems are consistent. But we can't actually prove it; it's ultimately an empirical question (and actually it would be even without the incompleteness theorem; if strong consistent formal system could prove their own consistency, that wouldn't make them any different from strong inconsistent formal systems).
Though as far as empirical questions go, the consistency of certain formal systems fundamental to human math does seem to be extremely probable.