I agree. but I think that there is no clear correlation between education and intellligence. education is required this is correct ,but that will not "always" prove that you are intelligent even if you have high education.
I get what you're trying to say. I know of a few Ph.D's who are complete social dropouts and totally incapable of performing many basic tasks that require intelligence outside of their field of expertise.
We are likely born with an already installed IQ, which can be measured in early childhood. If it happens to be much under 100 then we've been dealt a bad hand and usually won't go on to achieving a higher IQ.