Catch-22 (logic)

A catch-22 is a paradoxical situation in which an individual cannot avoid a problem because of contradictory constraints or rules. Often these situations are such that solving one part of a problem only creates another problem, which ultimately leads back to the original problem. Catch-22s often result from rules, regulations, or procedures that an individual is subject to but has no control over.

The term catch-22 was coined by Joseph Heller in his novel Catch-22.

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. This will only happen if he is evaluated by the squadron's flight surgeon and found "unfit to fly." "Unfit" would be any pilot who is willing to fly such dangerous missions, as one would have to be mad to volunteer for possible death. However, to be evaluated, he must request the evaluation, an act that is considered sufficient proof for being declared sane. These conditions make it impossible to be declared "unfit."

The "Catch-22" is that "anyone who wants to get out of combat duty isn't really crazy." Hence, pilots who request a mental fitness evaluation are sane, and therefore must fly in combat. At the same time, if an evaluation is not requested by the pilot, he will never receive one and thus can never be found insane, meaning he must also fly in combat.

Therefore, Catch-22 ensures that no pilot can ever be grounded for being insane even if he is.

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 he is both insane (I), and requests an evaluation (R));
2. $(I\rightarrow \neg R)$ (Premise: If a person is insane (I), he should not realize that he is, 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 people must either not be insane, or not request an evaluation)
4. $(\neg (I\land R))$ (3, De Morgan: since all people must either not be insane, or not request an evaluation, it follows that no person is both insane and requests an evaluation)
5. $(\neg E)$ (4, 1, Modus Tollens: since a person may be excused from flying only if he is both insane and requests 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

Besides referring to an unsolvable logical dilemma, Catch-22 is invoked to explain or justify the military bureaucracy. For example, in the first chapter it requires Yossarian to sign his name to letters that he censors while he is confined to a hospital bed. One clause mentioned in chapter 10 closes a loophole in promotions, which one private had been exploiting to reattain the attractive rank of Private First Class after any promotion. Through courts-martial for going AWOL, he would be busted in rank back to private, but Catch-22 limited the number of times he could do this before being sent to the stockade.

In chapter 6, Yossarian is told that Catch-22 requires him to do anything his commanding officer tells him to do, regardless of whether these orders contradict orders from the officer's superiors. In Chapter 39 an old woman relates that soldiers had claimed that the actual text of Catch-22 did not have to be revealed when carrying out orders related to it, meaning that "they have a right to do anything we can't stop them from doing." This exchange convinces Yossarian that Catch-22 does not even exist, but because the powers that be claim it does, and the world believes it does, it nevertheless has potent effects. Indeed, because it does not exist there is no way it can be repealed, undone, overthrown, or denounced.

At one point, Captain Black pressures Milo into depriving Major Major of food based on fabricated charges by comparing the situation to Catch-22. He asks, "You're not against Catch-22, are you?" Captain Black wants Major Major punished for not signing a loyalty oath, despite never having given Major the opportunity to sign it.

At another point, after intercourse, Luciana explains to Yossarian that she cannot marry him because he is crazy for wanting to marry her, since she is not a virgin.

In chapter 40, Catch-22 forces Colonels Korn and Cathcart to promote Yossarian to Major and ground him rather than simply sending him home. They fear that if they do not, others will refuse to fly, just as Yossarian did.

Significance of the number 22

Main articles: Catch-22 § Explanation of the novel's title, and Catch-22

Heller originally wanted to call the phrase, and hence the book, by other numbers, but he and his publishers eventually settled on 22. The number has no particular significance; it was chosen more or less for euphony. The title was originally Catch-18, but Heller changed it after the popular Mila 18 was published a short time beforehand.

Situations which have logical similarities to a Catch-22

• Circular logic
• Cadmean victory - A victory leading to one's own ruin
• Game of Chicken – Two participants desire a positive outcome by taking an action, yet if taken by both the result is devastatingly negative.
• 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, each waiting for the other to finish.
• Double bind – a forced choice between two logically conflicting demands.
• False dilemma - a situation in which only two alternatives are considered, when in fact there are additional options
• Gift of the Magi – Where two people in love with each other sell their belongings to buy gifts for each other, only to end up giving gifts related to the belonging they have sacrificed. (ie. A man sells a pocket watch to buy a brush for his wife. The wife then sells her long beautiful hair to buy a chain for the man's pocket watch.)
• Hobson's choice – the choice between taking an option and not taking it.
• Irony
• Kobayashi Maru – a scenario involving a choice between death of civilians or of the civilians and the officers who try to save them.
• The Lady, or the Tiger? – a short story involving a princess who must make a decision in a no-win situation.
• Lesser of two evils principle – a choice between two undesirable outcomes.
• Necessary Evil – anything which, despite being considered to have undesirable qualities, is preferable to its absence or alternative.
• Morton's Fork – a choice between two equally unpleasant alternatives.
• No-win situation – real choices exist, but no choice leads to success.
• Paradox – a statement or group of statements that leads to a contradiction or a situation which defies intuition.
• Pyrrhic victory - a victory with such a devastating cost to the victor that it carries the implication that another such victory will ultimately cause defeat.
• Reductio ad absurdum
• Sophie's Choice – a choice between two equally beloved entities, one of which must be destroyed to preserve the existence of the other.
• The Trial – a novel by Franz Kafka.
• The Captain of Köpenick
• Winner's curse
• Zugzwang

See also

• List of paradoxes