He was educated at the City of London School and Balliol College, Oxford University.
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 was Professor of Ancient Philosophy, Oxford University, 1989–94.
He was Professor of Ancient Philosophy at the University of Geneva 1994–2002.
He taught at the University of Paris-Sorbonne in France, and took his éméritat in 2006.
He was elected a Fellow of the British Academy in 1987.
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 was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1999.
He was awarded an honorary doctorate by the Humboldt University of Berlin in 2012.
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).