The Kossmann family was of Jewish descent and they came from Germany before they settled in the Netherlands.
He was arrested during a raid, was sent to Vught concentration camp, and had to work for two-and-a-half years in Germany, together with his twin brother Alfred.
In 1954 Kossmann obtained his Ph.D. from Leiden University, with a doctoral thesis entitled La Fronde.
In an interview in 2007, his former student Frank Ankersmit gives a description of him: He had an unusually strong and fascinating personality -- I never met anyone even remotely coming close to what he was like.
Just to give you an idea: he was all that one might associate with François Guizot, very much aloof, very intelligent, both impossible to get close to and yet very much accessible and blessed with the rhetorical powers of a Pericles.
[1]Kossmann became member of the Royal Netherlands Academy of Arts and Sciences in 1961 and resigned in 1966.