What sex is the soul?

In today's 'In Our Time' programme on women's contribution to the Enlightenment it was suggested that Descartes' dualism, with its emphasis on the soul as separate from the body, might have contributed to more egalitarian attitudes to the education of women. This is in stark contrasts to the supposedly egalitarian Rousseau who said

The education of women should always be relative to that of men. To please, to be useful to us, to make us love and esteem them, to educate us when young, to take care of us when grown up, to advise, to console us, to render our lives easy and agreeable; these are the duties of women at all times, and what they should be taught in their infancy