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Catch 22 has become a term, inspired by Joseph Heller's novel Catch-22, describing a general situation in which A must have been preceded by B, and B have must been preceded by A. Symbolically, (~B => ~A) & (~A => ~B) where either A or B must come into being first. A familiar example of this circumstance occurs in the context of job searching. In moving from school to a career, one may encounter a Catch 22 where one cannot get a job without experience, but one cannot get experience without a job. In this respect, the initial move to the job market can be very challenging.
Note that this common use of the term represents a slightly different problem from the prime example in the novel. The prototypical Catch 22 considers the case of a bombardier who wishes to be excused from combat flight duty. In order to be excused from such duty, however, he must submit an official medical diagnosis from the "flight surgeon", demonstrating that he is unfit for such hazardous (combat) flight duty because he is insane. However, according to Army regulations, any sane person would naturally not want to fly combat missions because they are so dangerous (any sane person would not want to fly at all).
By requesting permission not to to fly combat missions, on the grounds of insanity, the bombardier demonstrates that he is in fact sane and therefore is fit to fly.
Explaining the "catch", the flight surgeon, who fears making any official waves will get him transferred to a more dangerous theatre of the war, refuses to even consider filing such a medical opinion, because Catch 22 would render it ineffective anyway.
Conversely, any flyer who wishes to fly on combat runs implicitly demonstrated that he was insane and was unfit to fly and ought to be excused. Naturally, such flyers never submitted such requests. Of course, if they did, the "catch" would assert itself, short-circuiting any such attempt to escape from combat duty.
The fictional "catch", called in the novel Catch 22 in US Army Air Corps parlance, gives its name to the novel which is about the basic illogicality of war even in the way it was waged in "modern times" (the book was published only 15 years after World War II, and was therefore considered a commentary on modern war and current events).
This is symbolized as C (being excused from flying) necessitates A (a request) and ~B (not being insane, without which there would be no request) and A also necessitates B (being insane, which must be the basis for the request). Symbolically, ((A => ~B) & (A => B)) => C or, more simply, (A => ~B & B) => C).
The term is also sometimes informally, and inaccurately, used to represent logical conundrums that match neither of the above patterns. An example would be the chicken or the egg problem.
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