If asked to come up with a definition of play-writing chutzpah, I could do no better than this: Bring together two of the 20th century’s greatest intellectuals. (They didn’t actually meet, but never mind.) Compose an imagined, lively conversation between them about nothing less than life, death and the nature of belief. And make it a 75 minute one-act.

Unfortunately, this is not a hypothetical. In Mark St. Germain’s Freud’s Last Session, we meet the father of psychoanalysis in his London home. It’s September 1939; Germany’s invasion of Poland is a matter of international urgency and Britain has declared war that very day. But octogenarian expatriate Sigmund Freud, stricken with cancer, is more preoccupied with his own mortality. Freud is intrigued by the ideas of C. S. Lewis, the novelist, essayist and Oxford don, and invites the younger man over for a conversation. (This encounter is entirely St. Germain’s invention, though most of the rest of the script is historically accurate.)

If you’re familiar with the two figures, you already know that sparks will fly. Freud was a staunch atheist, though not humorless on the subject. Lewis was a nonbeliever for much of his life, but had recently embraced Christianity with the fervor sometimes seen in adult converts. As one might expect, the conversation often veers into questions of God, Christianity and existence.

Well, here’s my theater critic’s belief system: God is in the details. In this show, He manifests Himself chiefly in David P. Gordon’s marvelous set, a scrupulous recreation of Freud’s study filled with enough tchotchkes to keep Antiques Roadshow on the air till the next millennium. (I’d move in tomorrow if I could.)

If only the rest were on that level. It isn’t.

St. Germain imagines the dialogue between two titanic thinkers in a way that only a hack writer could, turning it into a stream of platitudes and cute aphorisms. (“The greatest problem with Christianity is Christians,” says Lewis, in typical St. Germain style.) Lest the mood get too somber, there are a few fart jokes and some sexual innuendo (the latter not quite sophisticated enough to qualify as double entendre — I’d give it a 1.5 at best). At its worst, Last Session veers into the kind of cranky-sitcom-character depiction more suited to I’m Not Rappaport. Sadly, it’s precisely at these moments that the audience seems most entertained.

Arden’s production doesn’t overcome the script — it sinks to the same level. David Howey’s heavily accented Freud nails every punch line. Though the character is 83 years old and riddled with cancer — in reality, Freud died only weeks after the play is set — Howey has enough showman’s energy to light London through the Blitz. It’s a skillful turn, certainly, but one that borders on vaudeville. Todd Scofield’s C. S. Lewis is less flashy — both the character and the performance — and he projects a winning sweetness.

But nearly every element in Ian Merrill Peakes’ production feels cranked-up. There are hardly any moments when the characters relax and suggest the natural rhythm of conversation — and, more critically, the thoughtful reflection these topics deserve. There’s far too much shouting for the intimate setting of the Arden’s Arcadia Stage, and in what proves an apt metaphor for the whole production, the lighting is too bright, banishing any sense of shadow or mystery. Gordon’s lovely room deserves better.

It’s strange how theaters seem to work in parallel sometimes: The Arden gives us this Borscht Belt psychoanalysis at the same time that, across town, Philadelphia Theatre Company’s Stars of David gives us the Jewish experience with rim shots from the Upper West Side. Has Center City suddenly become the Catskills resort comedy circuit? Maybe next season, the two companies should collaborate on Moses and Monotheism: The Musical.

Through Dec. 23, $36-$48, Arden Theatre, 40 N. Second St., 215-922-1122, ardentheatre.org.