 The results of the Hilbert school were not published because contradictions and paradoxes were regarded as symptoms of growth and as temporary difficulties. The diagnosis was that traditional logic is insufficient and the theory of concept-formation needs to be sharpened. Any concept \(C\) is given in a network of concepts (letter of Hilbert to Frege, Dec. 27, 1899; see Frege 1976, pp. 79–80), and this network is determined by the axioms. Only the consistency of the axioms that define the concept guarantees the legitimacy of \(C\). In a nutshell: paradoxes tell us that we must develop a metamathematical analysis of the notions of proof and of the axiomatic method; their importance is methodological as well as epistemological.