Catch-22 (logic)

A catch-22 is a paradoxical situation in which an individual cannot or is incapable of avoiding 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. Initially this is based on the explanation of the character Doc Daneeka as to why any pilot requesting a psych evaluation hoping to be found not sane enough to fly, and thereby escape dangerous missions, would thereby demonstrate his sanity:

"You mean there's a catch?"

"Sure there's a catch", Doc Daneeka replied. "Catch-22. Anyone who wants to get out of combat duty isn't really crazy."

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) because of mental illness, 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 for reasons of insanity)

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.

At another point in the book, a prostitute explains to Yossarian that she cannot marry him because he is crazy, and she will never marry a crazy man. She considers any man crazy who would marry a woman who is not a virgin. This closed logic loop clearly illustrated Catch-22 because by her logic, all men who refuse to marry her are sane and thus she would consider marriage; but as soon as a man agrees to marry her, he becomes crazy for wanting to marry a non-virgin, and is instantly rejected.

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 attempts to pressure Milo into depriving Major Major of food as a consequence of not signing a loyalty oath that Major Major was never given an opportunity to sign in the first place. Captain Black asks Milo, "You're not against Catch-22, are you?"

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 with logical similarities to a Catch-22

• Begging the question
• 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.
• Circular reasoning
• 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.
• Deal with the Devil – a cultural motif related to society, morals and religion, best portrayed in Faust, in which a dangerous bargain is struck between a person and Satan, with the human soul in eternal damnation as payment.
• 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. (i.e. A man sells a pocket watch to buy a brush for his wife. The wife had sold her long beautiful hair to buy a chain for the man's pocket watch.)
• Hobson's choice – the choice between taking what is offered and taking nothing. (After James Hobson, owner of a livery stable who required his customers to take the horse nearest the door.)
• Kobayashi Maru – a scenario involving a choice presented to a cadet in Star Trek where they either violate military regulations concerning the rendering of aid to a freighter crippled by a mine and in imminent threat of destruction, or violating the terms of a peace treaty by crossing into enemy territory (where the freighter lies in distress), risking one's company & crew to attempt to save the crippled freighter, and committing an act of war in the process of violating that treaty.
• 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.
• Mu - a question that is founded on incorrect or irrelevant assumptions.
• No-win situation – real choices do exist, but no choice leads to success. (See Kobayashi Maru.)
• Paradox – a statement or group of statements that leads to a contradiction or a situation which defies intuition.
• Pyrrhic victory - a success which is especially costly. (After King Pyrrhus, who sustained such heavy losses when he fought against, and won over, a Roman army that he is said to have complained, "Another such victory, and I am undone!")
• Social trap - a situation in which a group of people act to obtain short-term individual gains, which in the long run leads to a loss for the group as a whole
• Sophie's Choice – a choice between two equally beloved entities, one of which must be destroyed to preserve the existence of the other.
• Vicious circle - essentially the same as a Catch-22
• The Captain of Köpenick
• Winner's curse
• Zugzwang

See also

• Ironic process theory
• List of paradoxes