mushroom comments on What false beliefs have you held and why were you wrong? - Less Wrong Discussion
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Before I started tutoring I believed that anyone can learn first year math and science if only they put in the time and effort. Before I went to grad school I believed that I can learn all the advanced math and theoretical physics topics I was interested in. Neither belief survived experimental testing.
A lower bound on your first claim: Most everyone accepts that there exist people with severe intellectual disability. For many causes, the degree of impairment may range smoothly from severe into the "normal" range, where the bright lines are imposed by functional requirements like living independently or managing health care, and not by any well-defined abstract mental capability.