He taught for 25 years at Oxford University before moving to the University of Geneva. He was a Fellow of Oriel College, Oxford, 1968–78; a Fellow of Balliol College, Oxford, 1978–94, and has been Emeritus Fellow of Balliol College since 1994.
He is an expert on ancient Greek philosophy, and has edited the two-volume collection of Aristotle's works as well as a number of commentaries on Aristotle, the pre-Socratics and other areas of Greek thought.
He married in 1965 and has two daughters.
He is the brother of the novelist Julian Barnes, and he and his family feature in the latter's memoir Nothing to be Frightened Of (2008).
Barnes holds that our modern notion of the scientific method is "thoroughly Aristotelian." He emphasizes the point in order to refute empiricists Francis Bacon and John Locke, who thought they were breaking with the Aristotelian tradition. He claims that the "outrageous" charges against Aristotle were brought by men who did not read Aristotle's own works with sufficient attention and who criticized him for the faults of his successors.