RIDGEFIELD, Conn. — Everyone wants to ask Dick Cavett the same question, and it is a question that he never wants to answer: Of all today’s talk-show hosts, who is the “next Dick Cavett”?

“Well, that’s an awkward subject matter for me, because I know all of them,” Mr. Cavett, 81, said on a recent sunny Thursday afternoon at his sprawling country house in Connecticut. “I’m not addicted to talk shows. God knows, I’ve spent enough time on them.”

As in Mr. Cavett’s 1960s and ’70s heyday, the country is in a period of turbulence, with racial tensions flaring, protests in the streets, and a fundamental ideological fissure. The hosts who have emphasized substance, who have “gone political,” have been praised and nominated for Emmys.

But “the next Cavett”? Is such a thing possible?

If only.

For three decades, Mr. Cavett was the thinking person’s Johnny Carson, embodiment of an East Coast sophisticate. He wore smart turtlenecks and double-breasted blazers, had more cultural references than a Google server and laced martini-dry witticisms into lengthy, probing talks with 20th-century luminaries including Bette Davis, James Baldwin, Mick Jagger and Jean-Luc Godard.