Catch-22 Definition

the concept entry from Wikipedia:

A Catch-22, coined by Joseph Heller in his novel Catch-22, is a logical paradox wherein an individual finds him or herself in need of something that can be had only by not being in need of it. It is often spoken in regards to rules, regulations, procedures, or situations in which one has knowledge of being or becoming a victim but has no control over it occurring.

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 duty. To be grounded, he must be officially evaluated by the squadron's flight surgeon and then found "unfit to fly."

"Unfit" would be any pilot who is actually willing to fly such dangerous missions: as one would have to be mad to want to take on such missions.

But the "problem" is that to be declared "unfit", he must first "ask for evaluation", which is considered as a sufficient proof for being declared "sane". These conditions make being declared "unfit" impossible.

The "Catch 22" is that "anyone who wants to get out of combat duty, isn't really crazy" [1] Hence, pilots who request a 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 (i.e. they 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 were.

A logical formulation of this situation is:
1. (Premise: If a person is excused from flying (E), that must be because he is both insane (I), and requests an evaluation (R));
2. (Premise: If a person is insane (I), he should not realize that he is, and would have no reason to request an evaluation)
3. (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. (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. (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)

Life is full of these.