I couldn't sleep last night and, like most people (I'm guessing - I haven't done a poll or anything), when faced with insomnia, I like to think about some of the great problems of analytic philosophy. "Does the set of all sets contain itself?" I wondered. Here is some of my reasoning presented in that most venerable of philosophical forms: the dialogue.
Bertrand: Does the set of all sets contain itself?
Freddie: Yes. Obviously. Otherwise it would be indistinguishable from the set of all sets except itself.
Bertrand: But, if the set of all sets contains itself, the copy of itself within itself also contains itself and so on.
Freddie: wtf! Mind = blown!
Bertrand: I thought you'd like that.
Freddie: So the set of all sets does not contain itself?
Bertrand: But if it does not contain itself then it is at least one set short and can't really be the set of all sets.
Ludwig: It's a meaningless question. Try counting sheep.
Bertrand: Pay attention Ludwig, he tried that here.
Freddie: He was much better in those days, look it's got a nice photograph and a little poem...