Catch-22 is a satiricall bnovell by Joseph Heller, first published in 1961. The novel is frequently cited as one of the great literary works of the Twentieth century.
The prototypical Catch-22, as formulated by Heller, considers the case of a U.S. Army Air Forces bombardier who wishes to be excused from combat flight duty. In order to be excused from such duty, he must submit an official medical diagnosis from his squadron's flight surgeon, demonstrating that he is unfit because he is insane. According to Army regulations, any sane person would naturally not want to fly combat missions because they are so dangerous. By requesting permission not to fly combat missions, on the grounds of insanity, the bombardier demonstrates that he is in fact sane and therefore is fit to fly. Conversely, any flyer who wished to fly on combat runs implicitly demonstrated that he was insane and was unfit to fly and ought to be excused, and to be excused this person would only need to submit a request. Naturally, such flyers never submitted such requests. Of course, if they did, the "Catch" would assert itself, short-circuiting any such attempt to escape from combat duty.
Another Catch-22 is depicted in a scene with Luciana and Yossarian. Luciana is distraught because no man will marry her because she is not a virgin. Yossarian offers to marry her, but she claims he is crazy for wanting to marry a non-virgin like herself and says she can't marry him.
In words, Catch-22 can be expressed as: "C requires (implies) A and B; If A then not B; If B then not A". In formal Propositional logic symbolism this can be expressed as "
". In this example, in order to leave the Air Corps (outcome 
), you must be both crazy (proposition 
) and request to leave (proposition 
). If you're crazy () then you won't request to leave i.e.(
). But if you do request to leave () then you're not crazy! i.e.(
). Thus you can never leave ( cannot occur).
My version of Catchh 22 (and someone asked in another thread what it was)
They can do anything to you that you can't stop them doing to you. 
This gives me nightmares! I failed elementary logic in college!!
MidnightVoice wrote:In words, Catch-22 can be expressed as: "C requires (implies) A and B; If A then not B; If B then not A". In formal Propositional logic symbolism this can be expressed as "