Catch-22 (logic)

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 must have 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 gain experience without a job.

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 U.S. Army Air Force bombardier who wishes to be excused from combat flight duty. In order to be excused from such duty, he must submit an official medical diagnosis from his squadron's flight surgeon, demonstrating that he is unfit 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. By requesting permission not to fly combat missions, on the grounds of insanity, the bombardier demonstrates that he is in fact sane and therefore is fit to fly.

Conversely, any flyer who wished 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 U.S. Army Air Force 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.

In other words, if you do ask to be excused, this is a sign of sanity, and yet you can't be excused if sane. If you do not ask to be excused, you must be insane, but cannot be excused unless you ask. This refers to the "damned if you do, damned if you don't" scenario.

The term is also sometimes informally used to represent logical conundrums that match neither of the above patterns. An example would be the chicken or the egg problem.

http://en.wikipedia.org/wiki/Catch-22