Not maths. I think it is just very very subtle abuse of logic that leads to a conundrum where a certain type of set has to be declared as both one type and the opposite type.
It’s actually just a subtle wording game - a riddle.
It is neither because it is not a set at all. It is a type of “square-circle” (which is not a shape at all).
It is both. It is defined as a set that contains (1), (2), (3) and itself. It is explicitly stated that it is abnormal and implicitly that it is normal. By saying that it is neither as well as by saying that it is not a set, we are contradicting its definition.
As I said in my previous post, I am talking about what the expression means (i.e. what that expression can be used to represent regardless of whether or not such things exist) and not what the things that can be represented by that expression are. You are focusing on the latter. Obviously, nothing can be represented by the expression “A set that contains itself”. Thus, those things that can be represented by that expression are certainly not sets – or anything else – because they do not exist so they can’t be anything.
I don’t think that how obvious something is changes the truth of what it is. So I think we will just have to agree to maintain our own bubbles on that issue. 