I’d read a lot about consciousness in the weeks leading up to our talk and he told me, courteously, that I shouldn’t have bothered. (I’m pretty sure I should have.) Everything I needed to understand the play was in the play, he said, and once I saw it, all of those headache-inducing pages on materialism and mysterianism and panpsychism (the idea that maybe consciousness is ubiquitous, that our cafe table might have feelings, too) would become clear. “You don’t need to know anything except to keep your ears open and if possible, your brain awake,” he said.

“The Hard Problem” probably began in the mid-90s when Mr. Stoppard read a debate between the philosopher John Searle (who receives a thanks in the published script) and the philosopher and cognitive scientist David J. Chalmers in The New York Review of Books, and clipped those articles out. He read a lot and he thought a lot and he came to realize that while most neuroscientists agree that the brain causes consciousness and that we’ll know how once math and science progress far enough, that answer “rather skips over of how the trick is done,” he said.

He prefers to believe in some immaterial element. It’s a belief that many of his plays quietly promote, that there is something else — call it love or grace or divinity — that shapes our ends. It’s the claim that Hilary (Adelaide Clemens), the young psychologist at the heart of “The Hard Problem” makes. “The God idea shoves itself to the front like a doctor at the scene of an accident, because when you come right down to it, the body is made of things, and things don’t have thoughts,” she says.

Plays do have thoughts, of course. Mr. Stoppard’s plays are packed with them. Great plays have something more.

Mr. Stoppard is the rare playwright — Shaw, Pirandello and Pinter are others — to have earned his own adjective. Stoppardian works take clever, comic approaches to complex ideas. Mr. Stoppard didn’t dispute this, though he called it “a slightly lazy way of summing me up.” (He also made a self-effacing joke: “If I were called Jones, I don’t think anyone would try to make an adjective out of it.”)