The problem I see is that intelligence is at large innate, someone with a 110 IQ bracket can't realisticly retest at an IQ of 140 unless you're training purely

The problem I see is that intelligence is at large innate, someone with a 110 IQ bracket can't realisticly retest at an IQ of 140 unless you're training purely on IQ tests. This puts a severe upper bound on what anyone can 'solve trough education' as someone with a first tested IQ of 140 requires zero education to achieve a retest of 140 AND has the ability train or educate themselves even further. The IQ test itself is as real of a problem someone can solve as any other hypothetical problem. So if you choose to define intelligence by education, then you're still selecting for innate intelligence plus someones work ethic. Which to me is silly because the education system itself already selects for that and IQ tests are carefully designed for innateness which is why retests or learning for an IQ test bars you from a valid score. I'm sure Intelligence is somewhere inbetween but we can barely solve for one variable at a time.