The lectures in the Summer Semester of 1920 ended with consistency proofs for extremely weak fragments of arithmetic. The question, made explicit in the Introduction to
(see p. 296) was then this: Can these consistency proofs somehow be extended to establish the consistency of increasingly stronger and thus mathematically more interesting systems? The lectures of 1921/22 and 1922/23 give a resoundingly positive answer. However, the ‘extensions’ require a remarkable mathematical/logical and methodological breakthrough that leads to Hilbert’s proof theory and his finitist consistency programme.