I think that intelligence is much more environmentally driven rather than genetic, though I don't have any proper references for that. I would argue that, in a properly functioning society, intellectualism, assuming it's strongly tied to wealth, wouldn't really be heritable beyond one generation.
Combating anti-intellectualism as a trend is probably more complicated than just trying to get the existing educated to have more children then the existing uneducated.
Combating anti-intellectualism as a trend is probably more complicated than just trying to get the existing educated to have more children then the existing uneducated.