 On the side of mathematical foundations, three chapters of Gerhard Hessenberg’s Bericht (1906) on the fundamentals of set theory are devoted to foundational questions. They contain interesting ideas about the philosophy of mathematics, which unfortunately cannot be discussed in detail here. For instance, Hessenberg underlines the distinction between set theoretic definitions which give criteria for effectively deciding membership in a given set, and definitions which don’t. Concerning Kronecker’s constructive criticism of the arithmetized continuum, he holds that, although each irrational number determines an infinite fraction and each infinite fraction possesses a formation rule (“Bildungsgesetz”), it is not true that such a rule is given by explicit finite means. For otherwise, we could derive (a form of) the paradox of finite denotation, i.e., were formation laws to coincide with definable ones, they would be at most denumerable and hence the reals would be denumerable, against Cantor’s theorem.