notriddle comments on Feeling Rational - Less Wrong
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Correct me if I read it wrong, but did you just say that induction doesn't work? I admit I don't know how to even begin arguing for induction, so you've got a great opportunity; give an actual argument, rather than just saying we live in "a world where counter-induction holds."
Also, while any phenomenon can be described by an infinite number of math equations, the more complicated ones are less likely to be true. See also, Occam's Razor. Obviously, this relies on probability theory, which was formulated by induction, but you did say "even if you believe that there are some magic objective facts" which I assumed to be induction, probability theory, etc.