Definition: The empty set E is a subset of S if every member of E is a member of S.

P (Proposition): E is a subset of S.

Proof: P is false if there are members of E which do not belong to S. There are no members of E which do not belong to S, so P is true.

Problem with proof: There are no members of E. So though I can talk about no members, I can’t talk about “no membersbecause member doesn’t exist,which”doesn’t refer to anything. The problem already occurs in the Definition: to say that “something that doesn’t existwhich” is meaningless, it says that something that isn’t, is. E may exist, but its members do not.is

Conclusion: E is not a subset of S