End of the World. Play by Arthur Kopit. Starring John Shea, Barnard Hughes, Linda Hunt. Directed by Harold Prince. ''End of the World'' is a play of uncommon commitment and courage. Arthur Kopit and company are living dangerously as they mingle satire, mock realism, and philosophic discourse to tackle the overriding issue of the age: the threat of nuclear destruction. For what it attempts, and what it achieves, the late arrival at the Music Box is a major event of this or any other season.
Mr. Kopit approaches the subject slyly by casting his playwright-hero Michael Trent as a sort of theatrical private eye, replete with trench coat and crushed felt hat. Trent (John Shea) explains that a dramatist is like a detective, always searching for clues. In the present instance, the writer-sleuth is approached by billionaire Philip Stone (Barnard Hughes). Stone wants his four-page outline on the nuclear question developed into a stage play.He is prepared to finance the project and keep a production running, even if it finds no audience response.
The genesis of ''End of the World'' reflects a similar offer Mr. Kopit actually received. According to a Playbill note, much of the content, particularly the second act, derives from interviews conducted by the author. Subtitled ''The Investigation,'' Act II plunges protagonist and spectator into a succession of Washington conversations in which Trent attempts to identify and comprehend the rationale for prevailing nuclear policy.
In the process, he encounters a series of dizzying and often hilarious rationalizations as expressed by his government sources. They include a Pentagon general (David O'Brien), a Soviet specialist (Jaroslav Stremien), two think-tank types who rattle off their spiels as they stuff Cookin' Good chickens for a gourmet lunch, and a shadowy figure who finally keeps a promised rendezvous.
Trent hears things like: ''A bluff taken seriously is much more serious than a serious threat taken as a bluff. . . . We have to learn how to wage nuclear war rationally. . . . What you have to do is out-preempt them. . . .''
Act III, ''The Discovery,'' returns Trent to his Stamford, Conn., home base to confront not only his impatient patron but the most rigorous phase of his Odyssey - the self-examination that brings ''End of the World'' to its own tentative conclusion. Trent recalls an incident, years before, when he was left alone for the first time with his newborn son. It is a terrifying and eventually moving statement. With this speech, Mr. Shea brilliantly caps his tireless performance of a demanding role.
The speech is counterpointed by Stone's description of an experience during a Pacific A-test (a section credited to Robert Scheer's book ''With Enough Shovels''). Here as elsewhere, Mr. Hughes demonstrates the solidity of his contribution as the mysterious, apparently imperturbable patron. In the real-life role of a talent representative, Audrey Wood (Mr. Kopit's agent before her prolonged illness), Linda Hunt presides with a blend of solicitude and acumen which shames her crassly comic fellow agents (Richard Seff and Mr. O'Brien). (Mr. Kopit enjoys these showbiz vaudeville bits.)
Harold Prince has staged the production with an extraordinary sensitivity to the dense complexity of themes and counterthemes that make ''End of the World'' so difficult a work. Always a tricky business, the play-within-a-play is here complicated by Mr. Kopit's satirical, private-eye approach to a most serious subject.
Clarke Dunham's series of background panels provides the well-ordered areas onto which Mr. Dunham and Lisa Podgur's breathtaking projections are exposed. These include two Escher prints - with cunning manipulation of perspective - that provide a visual commentary on the nuclear argument: the arrival by logical means at preposterous conclusions. The fluidly changing slides are more than mere embellishments to a theater work that stirs imagination and stimulates thought.