The bulk of this volume consists of six sets of notes for lectures Hilbert gave (often in collaboration with Bernays) on the foundations of mathematics between 1917 and the early 1930s. The notes detail the increasing dominance of the metamathematical perspective in Hilbert's treatment, i.e., the development of modern mathematical logic, the evolution of proof theory, and the parallel emergence of Hilbert's finitist standpoint. The notes are mostly very polished expositions; e.g., the 1917-18 lectures are in effect a first draft of Hilbert and Ackermann's "Grundzuge der theoretischen Logik" (1928), reprinted in this Volume. They are thus essential for understanding the development of modern mathematical logic leading up to Hilbert and Bernays's "Grundlagen der Mathematik" (1934, 1938). Also included is a complete version of Bernay's "Habilitationschrift" of 1918, only partially published in 1926.
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