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An Nonempty Thread about the Empty Set
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It& #39;s well known that the topologist R.L. Moore didn& #39;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& #39;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& #39;s student, he, like everyone else there, was exposed to Moore& #39;s ideas. He told me the following story. (3/6)
I can& #39;t remember if he himself was the student in question or if it was someone else. It doesn& #39;t really matter, so I& #39;ll tell it like this.
Student: Professor Etlinger, I am very confused about the empty set.
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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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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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