Why is it ill-defined? As you said, there's no contradiction.
replyAlso, in the usual ZF set theory, it's empty.
It’s ill-defined because it doesn’t uniquely define the set. There are at least two different sets that D could be (one containing it and one not containing it), hence the expression doesn’t denote a well-defined set.
replyThe axioms of ZF do not allow to form that expression, so the set doesn’t exist in ZF.
... and, as such, it doesn't contain itself!
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