Plato's woman problem

In The Republic, Plato outlines a role for women in his ideal society that seems revolutionary, i.e. that they should occupy the highest position in public life. In Athenian society at the time, women were completely excluded from politics, so this is a radical proposal. But elsewhere, Plato expresses doubt about women’s natural abilities. What did he really think? And how does this tension persist today for women in philosophy?