 Concerning the subsequent developments in connection with logic, the process of streamlining the tools of logic steadily continued in Göttingen through the work of Hilbert and his school. This is especially clear from his unpublished lecture notes (e.g., those of Winter-Semester course 1917–1918 Prinzipien der Mathematik), which are in many respects close to the textbook of Hilbert-Ackermann of 1928 and which contain formulations of first and second order logic, together with ramified type theory and the axiom of reducibility. Paradoxes are derived by allowing a suitable form of unrestricted comprehension; the problematic assumption is located in the admissibility of predicates and propositions as objects, i.e., formally in the expressions \(X(Y), P(P)\). Variants of the traditional Liar and of the Berry antinomy are introduced. Interestingly, Hilbert sticks essentially to type theory (he does not lecture upon Zermelo’s system); he defines the ramified theory of types with the axiom of reducibility, proving that certain parts of mathematics can be carried out in the system (on Russell’s influence, see Mancosu 2003).