I recently heard about mathematical paradoxes and I have a perhaps strange question: It seems to me that the goal is to figure out what the fundamental problem is, i.e. what gives rise to the paradox, so we can perhaps rewrite the axioms so that the problems disappear. But why not just say: "Well, paradoxes arise when you talk about sets that contain every set, so let's avoid talk about sets that contain empty sets." (Kind of like saying that bad things happen when you divide something with zero, so don't do it!)