I don’t know if Chris and captainfalcon remember this, but there was once a time when I was trying to recall a particular logical paradox that deals with self-referencing statements. We got into this discussion because of the book Godel, Escher and Bach. I ran across a similar paradox recently. Here it is.
If A is the set which contains all sets that do not contain themselves, then does A contain A?
Neither “yes” nor “no” work as answers.