Catch-22 is both a novel by Joseph Heller and a logic problem of the same name.
Heller's novel is set on an American airbase in Italy during the Second World War, and tells the story of Captain Yossarian, a bombardier in the Army Air Corps who wants to be discharged. The only way he can be discharged is by claiming that the war has made him insane. However, the camp's doctor points out that Yossarian's desire to be discharged (and thus safe) proves his sanity. Thus, Yossarian is caught in a paradoxical situation.
The nature of this situation is the titular "Catch-22." The term has grown to describe any problem which seemingly has multiple solutions, but in which each possible solution creates a new condition that makes it impossible - leaving only the original problem once more. For example, elsewhere in the novel, a character is accused of being disloyal to his country for refusing to sign a loyalty oath, only to be told it is also disloyal to request to take a loyalty oath. Even though it appears he could simply swear the oath, in fact a Catch-22 ensures he will be seen as disloyal no matter what he does.
The Heller novel addresses not only the inhumanity and insanity of war, but the ways in which large corporate organisations such as armies are able to thrive because of the ways in which they create their own internal logic. It has remained a popular work ever since its publication.
“”There was only one catch and that was Catch-22, which specified that a concern for one's safety in the face of dangers that were real and immediate was the process of a rational mind. Orr was crazy and could be grounded. All he had to do was ask; and as soon as he did, he would no longer be crazy and would have to fly more missions. Orr would be crazy to fly more missions and sane if he didn't, but if he was sane he had to fly them. If he flew them he was crazy and didn't have to; but if he didn't want to he was sane and had to. Yossarian was moved very deeply by the absolute simplicity of this clause of Catch-22 and let out a respectful whistle.