Apropos of Mr. Rauschenberg, Cage once said, “Beauty is now underfoot wherever we take the trouble to look.” Cage meant that people had come to see, through Mr. Rauschenberg’s efforts, not just that anything, including junk on the street, could be the stuff of art (this wasn’t itself new), but that it could be the stuff of an art aspiring to be beautiful — that there was a potential poetics even in consumer glut, which Mr. Rauschenberg celebrated.

“I really feel sorry for people who think things like soap dishes or mirrors or Coke bottles are ugly,” he once said, “because they’re surrounded by things like that all day long, and it must make them miserable.”

“Screwing things up is a virtue,” he said when he was 74. “Being correct is never the point. I have an almost fanatically correct assistant, and by the time she re-spells my words and corrects my punctuation, I can’t read what I wrote. Being right can stop all the momentum of a very interesting idea.”

This attitude also inclined him, as the painter Jack Tworkov once said, “to see beyond what others have decided should be the limits of art.”