The core of Volume3 consists of lecture notes for seven sets of
lectures Hilbert gave (often in collaboration with Bernays) on the
foundations of mathematics between 1917 and 1926. These texts make
possible for the first time a detailed reconstruction of the rapid
development of Hilbert's foundational thought during this period,
and show the increasing dominance of the metamathematical
perspective in his logical work: the emergence of modern
mathematical logic; the explicit raising of questions of
completeness, consistency and decidability for logical systems; the
investigation of the relative strengths of various logical calculi;
the birth and evolution of proof theory, and the parallel emergence
of Hilbert's finitist standpoint. The lecture notes are accompanied
by numerous supplementary documents, both published and
unpublished, including a complete version of Bernays's
"Habilitationschrift" of 1918, the text of the first edition of
Hilbert and Ackermann's "Grundzuge der theoretischen Logik" (1928),
and several shorter lectures by Hilbert from the later 1920s. These
documents, which provide the background to Hilbert and Bernays's
monumental "Grundlagen der Mathematik" (1934, 1938), are essential
for understanding the development of modern mathematical logic, and
for reconstructing the interactions between Hilbert, Bernays,
Brouwer, and Weyl in the philosophy of mathematics. "
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