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).
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).
Ah, good point. I’d forgotten about that part. IIRC he first noted that and then expanded out the details to see where the problem was.