And note also that even Russell's paradox was not phrased originally in this way. His original phrasing as I understand it rested on taking the set of all sets A and then looking at the cardinality of that set's powerset P(A). Then we have |P(A)| > |A| but P(A) <= A so |P(A)| <= |A| which is a contradiction. This is essentially the same as Russell's paradox when one expands out the details (particularly, the details in the proof that in general a set has cardinality strictly less than its powerset).