Mathematics

No two sets can have the same conditions for membership, so if Miss X is in the set of young girls because she's a young girl, then she cannot be in the set of female humans because she's a young girl. Paradox?

Comments

If there is a paradox here, I

If there is a paradox here, I don't think it will have anything to do with a conflict in the conditions for set membership. Let's leave aside that there may be sorites-style paradoxes arising from the vagueness of the predicates "young girl" and even "female human." I suspect that those paradoxes can be solved in the "epistemicist" way (see this link).

One and the same individual can possess various mutually consistent properties: she can be a young girl (at a specified time t), a female human being (at any time during her existence, including at time t), and so on. So Miss X can belong to the set of girls who are young at t, the set of female human beings, the set of human beings, the set of mammals, the set of things referred to by you in your question above, etc. She would belong to each of those different sets for different but compatible reasons. I don't see anything paradoxical about that.

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