For the Unread -- Catch 22

Catch-22 is a term coined by Joseph Heller in his novel Catch-22, describing a false dilemma in a rule, regulation, procedure or situation, where no real choice exists. In probability theory, it refers to a situation in which multiple probabilistic events exist, and the desirable outcome results from the confluence of these events, but there is zero probability of this happening, as they are mutually exclusive.

Logic

The prototypical Catch-22, as formulated by Heller, involves the case of John Yossarian, a U.S. Army Air Forces bombardier, who wishes to be excused from combat flight duty. In order to be excused, he must submit an official medical diagnosis from his squadron's flight surgeon, demonstrating that he is unfit to fly because he is insane. In order to get the diagnosis, he must approach the surgeon to ask for one.

However, “catch 22” — the twenty-second of the guidelines used by military surgeons to “catch” those falsely claiming to be insane — is that an insane person should not believe or suspect that they are insane. Thus, to be recognised as insane, a person must not ask for an evaluation, because doing so implicitly shows that they suspect themselves to be insane. But, if a person does not ask for an evaluation, they cannot be recognised as insane because the evaluation is the method by which such recognition would occur. Thus, nobody can ever classify themselves as insane (even if they genuinely are), and thus nobody may ever use an insanity diagnosis to escape flying combat missions, ignoring the possibility of someone else recommending an evaluation for a peer.