# Catch-22 (logic)

"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.

A logical formulation of this situation is:

:1. $\left(E Rightarrow \left(I land R\right)\right)$ (Premise: If a person is excused from flying (E), that must be because they are both insane (I), and request an evaluation (R));:2. $\left(I Rightarrow eg R\right)$ (Premise: If a person is insane (I), they should not realise that they are, and would thus have no reason to request an evaluation):3. $\left( eg I lor eg R\right)$ (2, Definition of implication: since an insane person would not request an evaluation, it follows that all persons must either not be insane, or not request an evaluation):4. $\left( eg \left(I land R\right)\right)$ (3, De Morgan: since all persons must either not be insane, or not request an evaluation, it follows that no person can be both insane and request an evaluation):5. $\left( eg E\right)$ (4, 1, Modus Tollens: since a person may be excused from flying only if they are both insane and request an evaluation, but no person "can" be both insane and request an evaluation, it follows that no person can be excused from flying)

The above describes the concept commonly referred to by the phrase “Catch 22”. The book adds an element of complete absurdity to the situation, adding that the same regulations also stipulate that (because flying combat missions is so dangerous) any sane person would not willingly fly combat missions. Thus, any person who flies missions "must" be insane and thus should only need to be evaluated in order to be excused from flying. However, because requesting an evaluation is a sign of sanity, no pilots are grounded for insanity. The “catch 22” statement is the only reason anyone is in the air at all.

Other uses from the novel

The novel contains several examples of the Catch-22 regulation and other similar situations. One example occurs when 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 a crazy man.

In another Catch-22, Orr tells Yossarian that Appleby has flies in his eyes. Appleby supposedly cannot realize that he has flies in his eyes because the very fact means that his vision is clouded, making it impossible for him to see anything clearly, including whether or not he has flies in his eyes. Appleby doesn't realize that he has clouded vision either, and therefore has no way of knowing he has flies in his eyes.

Major Major creates a Catch-22 when he instructs his sergeant that no-one may come in and see him, unless he is not in. If he "is" in, people must be told to wait — until he has left.

Besides being an unsolvable logical dilemma, Heller's text contains two more distinct clauses of Catch-22. In the first chapter, officers who censor the privates' letters must sign their own name according to Catch-22, and in the final chapters it is restated simply as “anything can be done to you that you can not prevent”. The latter clause, in some instances, provides a solution to Catch-22, which Heller describes by borrowing the Prussian expression, "die Flucht nach vorne antreten" (“to take flight [flee] forward”). In the case of Orr, a friend of Yossarian (Heller’s main character), this was done by deserting and fleeing to Sweden.

Popular culture example

In a famous retort to U.S. country clubs of the period not accepting minorities as members, Groucho Marx, in claiming a club had made him an exception, quipped “I sent the club a wire stating: "Please accept my resignation. I don’t want to belong to any club that will accept me as a member."”

Here, Marx is either not a member of a club, or if a club would accept him, he would immediately resign on the grounds that it would accept him. This leaves Marx completely unaffiliated no matter what – while he might wish to join a club, his acceptance would immediately cause him to leave.

ee also

"Similar to a Catch-22:"
*Circular logic
*False dilemma
*Irony
*No-win situation — real choices exist, but no choice leads to success.
*The Lady and the Tiger — a short story involving a princess who must make a decision in a false dilemma situation.

"Sometimes confused with a Catch-22:"
*Chicken or the egg — a seemingly unbreakable cycle of causation, which has an unknown origin.
*Cornelian dilemma — a choice between actions which will all have a detrimental effect on the chooser or on someone they care for.
*Deadlock — in computing, when two commands reach a standstill or impasse; paradoxically waiting for the other to finish.
*Double bind — a forced choice between two logically conflicting demands.
*Hobson’s choice — the choice between taking an option or not taking it.
*Lesser of two evils principle — a choice between two undesirable outcomes.
*Morton’s Fork — a choice between two equally unpleasant alternatives.
*Paradox — often mistakenly used to describe situations that are ironic.

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