Catch-22 (logic) - Logic

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. (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. (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 for reasons of insanity)