Alan Arkin played Yossarian in the 1970 movie.
Catch-22 is a satirical World War 2 novel written in 1961 by Joseph Heller that contains a logical paradox called Catch-22. The anti-hero of this serious and comic book is Capt. Yossarian, whose main motivation is to stay alive despite the absurdity of military bureaucracy and the insanity of war. Here's the scene in the novel that explains the catch:
...Yossarian came to him one mission later and pleaded again, without any real expectation of success, to be grounded...Catch-22, Wikipedia>>
“You’re wasting your time,” Doc Daneeka was forced to tell him.
“Can’t you ground someone who’s crazy?”
“Oh, sure, I have to. There’s a rule saying I have to ground anyone who’s crazy.”
“Then why don’t you ground me? I’m crazy. Ask Clevinger.”
“Clevinger? Where is Clevinger? You find Clevinger and I’ll ask him.”
“Then ask any of the others. They’ll tell you how crazy I am.”
“Then why don’t you ground them?”
“Why don’t they ask me to ground them?”
“Because they’re crazy, that’s why.”
“Of course they’re crazy,” Doc Daneeka replied. “I just told you they’re crazy, didn’t I? And you can’t let crazy people decide whether you’re crazy or not, can you?”
Yossarian looked at him soberly and tried another appraoch. “Is Orr crazy?”
“He sure is,” Doc Daneeka said.
“Can you ground him?”
“I sure can. But first he has to ask me to. That’s part of the rule.”
“Then why doesn’t he ask you to?”
“Because he’s crazy,” Doc Daneeka said. “He has to be crazy to keep flying combat missions after all the close calls he’s had. Sure, I can ground Orr. But first he has to ask me to.”
“That’s all he has to do to be grounded?”
“That’s all. Let him ask me.”
“And then you can ground him?” Yossarian asked.
“No. Then I can’t ground him.”
“You mean there’s a catch?”
“Sure there’s a catch,” Doc Daneeka replied. “Catch-22. Anyone who wants to get out of combat duty isn’t really crazy.”
There was only one catch and that was Catch-22, which specified that a concern for one’s own 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.
“That’s some catch, that Catch-22,” he observed.
“It’s the best there is,” Doc Daneeka agreed.