Call the painter Andrew Masullo anything you like, as long as you don’t call him an artist. “I don’t like the word,” he proclaimed one day last month, soon after welcoming me to his modest apartment cum studio here on the outskirts of the city. “Everybody is an artist nowadays, and it doesn’t mean anything anymore.”

“I’m not an artist,” Herzog said. “I’m a soldier.”

What does it mean that some of the most praised artists in the whitney biennial don’t want to be called “artists”?