An Nonempty Thread about the Empty Set

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It's well known that the topologist R.L. Moore didn't accept the existence of the empty set. For example, in his view, intersection is not totally defined: if two sets have no elements in common, then they simply don't intersect. (2/6)

My adviser got his PhD from Texas in 1958 under the direction of Hyman Joseph Etlinger. Although he was not Moore's student, he, like everyone else there, was exposed to Moore's ideas. He told me the following story. (3/6)

I can't remember if he himself was the student in question or if it was someone else. It doesn't really matter, so I'll tell it like this.

Student: Professor Etlinger, I am very confused about the empty set.

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Etlinger: Well, what I want you to do is to imagine the foulest, dirtiest, smelliest camel in the entire world.

S: OK

E: Now as an axiom, I tell you that this camel--who, I remind you, is very offensive to be around--is an element of every set.

S: OK

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E: And that means the set whose only element is that camel is a subset of every set, right?

S: Yes

E: OK, but now that camel is just too smelly for us to be able to do anything with it. So let's just get rid of it. What's left behind is the empty set.

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