# Catch-22 (logic)

Catch-22 is a term coined by Joseph Heller in his novel Catch-22, describing a set of rules, regulations or procedures, or situation which presents the illusion of choice while preventing any real choice. 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 archetypal Catch-22, as formulated by Heller, involves the case of John Yossarian, a U.S. Army Air Forces bombardier, who wishes to be grounded from combat flight duty. To be grounded, he must be officially evaluated by the squadron's flight surgeon and found unfit to fly, which would be an automatic diagnosis of the insanity of any willing pilot because only a mad person would take on the missions, because of the danger. But to get the diagnosis he must ask for it, and in doing so shows he has enough sanity to try not to fly missions.

The “Catch 22” is that "anyone who wants to get out of combat duty isn't really crazy."[1] So pilots requesting an evaluation are not insane and therefore fit for combat duty, but those who don't ask will not be recognized because they have had no evaluation. Catch-22 ensures that no pilot can ever be grounded for being insane (even if they are).

A logical formulation of this situation is:

1. $(E \Rightarrow (I \land R))$ (Premise: If a person is excused from flying (E), that must be because they are both insane (I), and request an evaluation (R));
2. $(I \Rightarrow \neg R)$ (Premise: If a person is insane (I), they should not realise that they are, and would have no reason to request an evaluation)
3. $(\neg I \lor \neg R)$ (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. $(\neg (I \land R))$ (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. $(\neg E)$ (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)

## 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.

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 via the window.

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 is captured by the old German expression, die Flucht nach vorne antreten (“to take flight [flee] forward”): In the case of Orr, a friend of Yossarian (Heller’s main character), the solution was to desert and flee to Sweden, a solution that Yossarian ultimately adopts himself.

## Significance of the number 22

According to many sources[2] Heller originally wanted to call the phrase, and thence the book, by other numbers, but between himself and his publishers eventually settled on 22. The number has no particular significance it was chosen more or less for euphony.

### False dilemmas and circular logic

Situations which have logical similarities to a Catch-22.

### Non-false dilemma situations

Situations which may be confused with a Catch-22, but have quite different logic or outcomes.

• 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 processes 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 — a statement or group of statements that leads to a contradiction or a situation which defies intuition.

## References

1. ^ Joseph Heller (1999). Catch-22: A Novel. Simon and Schuster. p. 52. ISBN 9780684865133.
2. ^ [Joseph_Heller#Catch-22]