He was an intimate friend of Thrasea Paetus and Seneca, and was held in the highest estimation for his consistent disregard of creature comfort in the pursuit of virtue. His contempt for worldly prosperity is shown by his reply to Caligula who, wishing to gain his friendship, sent him a large present. He replied, "If Caligula had intended to bribe me, he should have offered me his crown."
Vespasian banished him, but Demetrius laughed at the punishment and mocked the emperor's anger. He reached the logical conclusion of Cynicism in attaching no real importance to scientific data.