Hilbert, David (Author)
Ewald, William (Editor)
Sieg, Wilfried (Editor)
Hallett, Michael (Editor)
Majer, Ulrich (Editor)
Schlimm, Dirk (Editor)
The core 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 The lecture notes are accompanied by numerous supplementary documents, both published and unpublished, including a complete version of Bernays's Habilitationschrift of 1918, the text of the first edition of Hilbert and Ackermann's Grundzüge der theoretischen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.
...MoreReview John W. Dawson (2016) Review of "David Hilbert's Lectures on the Foundations of Arithmetic and Logic, 1917--1933". Historia Mathematica (pp. 105-107).
Review Archibald, Tom (2015) Review of "David Hilbert's Lectures on the Foundations of Arithmetic and Logic, 1917--1933". Isis: International Review Devoted to the History of Science and Its Cultural Influences (pp. 480-481).
Article
Sieg, Wilfried;
(2014)
The Ways of Hilbert's Axiomatics: Structural and Formal
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Book
Gauthier, Yvon;
(2002)
Internal Logic: Foundations of Mathematics from Kronecker to Hilbert
(/isis/citation/CBB000301820/)
Article
Abrusci, V. Michele;
(2014)
On Hilbert's Axiomatics of Propositional Logic
(/isis/citation/CBB001213913/)
Book
Gabriele Lolli;
(2016)
Tavoli, sedie, boccali di birra: David Hilbert e la matematica del Novecento
(/isis/citation/CBB100106060/)
Article
Willea, Matthias;
(2011)
“Metamathematics” in Transition
(/isis/citation/CBB001211006/)
Article
Paseau, Alexander;
(2011)
Mathematical Instrumentalism, Gödel's Theorem, and Inductive Evidence
(/isis/citation/CBB001024149/)
Book
William Boos;
Florence S. Boos;
(2018)
Metamathematics and the Philosophical Tradition
(/isis/citation/CBB060593902/)
Chapter
Mancosu, Paolo;
Zach, Richard;
Badesa, Calixto;
(2009)
The Development of Mathematical Logic from Russell to Tarski, 1900--1935
(/isis/citation/CBB001210349/)
Chapter
David E. Rowe;
(2015)
Historical Events in the Background of Hilbert’s Seventh Paris Problem
(/isis/citation/CBB995513838/)
Book
Corry, Leo;
(2004)
David Hilbert and the Axiomatization of Physics (1898-1918): From Grundlagen der Geometrie to Grundlagen der Physik
(/isis/citation/CBB000550055/)
Article
Cerroni, Cinzia;
(2007)
The Contributions of Hilbert and Dehn to Non-Archimedean Geometries and Their Impact on the Italian School
(/isis/citation/CBB000930656/)
Article
Rédei, Miklós;
(2014)
Hilbert's 6th Problem and Axiomatic Quantum Field Theory
(/isis/citation/CBB001213911/)
Article
Cassou-Noguès, Pierre;
(2006)
Signs, Figures and Time: Cavaillès on “Intuition” in Mathematics
(/isis/citation/CBB000933621/)
Article
Stillwell, John;
(2014)
Ideal Elements in Hilbert's Geometry
(/isis/citation/CBB001213909/)
Article
Olga Hoppe-Kondrikova;
Lukas M. Verburgt;
(2016)
On A.ya. Khinchin's Paper ‘ideas of Intuitionism and the Struggle for a Subject Matter in Contemporary Mathematics’ (1926): A Translation with Introduction and Commentary
(/isis/citation/CBB951542109/)
Article
Karela, Catherine;
(2010)
Hilbert on Different Notions of Completeness: A Conceptual and Historical Analysis
(/isis/citation/CBB001220619/)
Article
McLarty, Colin;
(2011)
Emmy Noether's First Great Mathematics and the Culmination of First-Phase Logicism, Formalism, and Intuitionism
(/isis/citation/CBB001022015/)
Article
Li, Di;
(2005)
Transmission of the mathematical theories of German mathematicians in China during the first half of the 20th century
(/isis/citation/CBB000503127/)
Article
Rowe, David E.;
(2004)
Making Mathematics in an Oral Culture: Göttingen in the Era of Klein and Hilbert
(/isis/citation/CBB000500124/)
Article
Schirrmacher, Arne;
(2003)
Planting in his Neighbor's Garden: David Hilbert and Early Göttingen Quantum Physics
(/isis/citation/CBB000641699/)
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