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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 Hilberts 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 Ackermanns 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 Bernayss Grundlagen der Mathematik (1934, 1938). Also included is a complete version of Bernays Habilitationschrift of 1918, only partially published in 1926.
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This volume contains a selection of material exhibiting many of Hilberts philosophical and foundational views on particular theories and the exact sciences in general, drawn from his private notebooks and from lectures for more general audiences held in the 1920s.
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This volume focuses on notes for lectures on the foundations of the mathematical sciences held by Hilbert in the period 1894-1917. They document Hilbert's first engagement with 'impossibility' proofs; his early attempts to formulate and address the problem of consistency, first dealt with in his work on geometry in the 1890s; his engagement with foundational problems raised by the work of Cantor and Dedekind; his early investigations into the relationship between arithmetic, set theory, and logic; his advocation of the use of the axiomatic method generally; his first engagement with the logical and semantical paradoxes; and the first formal attempts to develop a logical calculus. The Volume also contains Hilbert's address from 1895 which formed the preliminary version of his famous Zahlbericht (1897).