Editing Catch-22 (logic) (section)

== Logic ==
The [[archetypal]] ''catch-22'', as formulated by [[Joseph Heller]], involves the case of [[John Yossarian]], a [[United States Army Air Corps|U.S. Army Air Forces]] [[Bombardier (air force)|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 [[Insanity|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".<ref name="Heller1999" /> 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:
{{Aligned table |cols=4
 |col1style=width:3.0em;text-align:center; |col2style=padding-right:1.0em; |col3style=width:47.0em;line-height:1.35em;padding-right:1.5em;
 | 1. | <math>(E \rightarrow (I \land R))</math>
      | For a person to be excused from flying on the grounds of insanity (E), he must both be insane (I) and have requested an evaluation (R). | ([[premise]])
 | 2. | <math>(I \rightarrow \neg R)</math>
      | An insane person (I) does not request an evaluation (¬R) because he does not realize he is insane. | (premise)
 | 3. | <math>(\neg I \lor \neg R)</math>
      | Either a person is not insane (¬I) or does not request an evaluation (¬R). | {{nowrap|(2. and [[Material implication (rule of inference)|material implication]])}}
 | 4. | <math>(\neg (I \land R))</math>
      | No person can be both insane (I) and request an evaluation (R). | (3. and [[De Morgan's laws]])
 | 5. | <math>(\neg E)</math>
      | Therefore, no person can be excused from flying on the grounds of insanity (¬E) because no person can be both insane and have requested an evaluation. | (4., 1. and ''[[modus tollens]]'')
}}

The philosopher Laurence Goldstein argues that the "airman's dilemma" is logically not even a condition that is true under no circumstances; it is a "[[Vacuous truth|vacuous]] [[Logical biconditional|biconditional]]" that is ultimately meaningless. Goldstein writes:<ref>{{cite book |first=Laurence |last=Goldstein |chapter-url=https://philpapers.org/rec/GOLTBR-2 |chapter=The Barber, Russell's paradox, catch-22, God, contradiction and more: A defence of a Wittgensteinian conception of contradiction |title=The law of non-contradiction: new philosophical essays |editor-first=Graham |editor-last=Priest |editor2-first=J. C. |editor2-last=Beall |editor3-first=Bradley |editor3-last=Armour-Garb |publisher=Oxford University Press |year=2004 |access-date=June 25, 2023}}</ref>

{{quotation|The catch is this: what looks like a statement of the conditions under which an airman can be excused flying dangerous missions reduces not to the statement

:(i) 'An airman can be excused flying dangerous missions if and only if Cont' (where 'Cont' is a contradiction)  
 
(which could be a mean way of disguising an unpleasant truth), but to the worthlessly empty announcement 
 
:(ii) 'An airman can be excused flying dangerous missions if and only if it is not the case that an airman can be excused flying dangerous missions' 
 
If the catch were (i), that would not be so bad—an airman would at least be able to discover that under no circumstances could he avoid combat duty. But Catch-22 is worse—a welter of words that amounts to nothing; it is without content, it conveys no information at all.}}