>there was a town in which the barber shaved all men who did not shave >themselves. Who shaved the barber?
There is nothing in this statement which precludes women in this town from shaving men. Perhaps the barber's wife shaves the barber. Is there a set of men who do shave themselves, but also shave others? Perhaps one of them shaves the barber.
Is ambiguity that which causes us to forget to consider all the possibilities? In that case I think some part of ambiguity must be in the eye of the beholder... not only in the language. I presume that would hold equally true for the language of mathematics as for any other language.