Book ID: CBB001551530

David Hilbert's Lectures on the Foundations of Arithmetic and Logic, 1917--1933 (2013)


Hilbert, David (Author)
Ewald, William (Editor)
Sieg, Wilfried (Editor)
Hallett, Michael (Editor)
Majer, Ulrich (Editor)
Schlimm, Dirk (Editor)


Publication Date: 2013
Physical Details: xxv + 1062 pp.; ill.
Language: English

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 The lecture notes are accompanied by numerous supplementary documents, both published and unpublished, including a complete version of Bernays's Habilitationschrift of 1918, the text of the first edition of Hilbert and Ackermann's Grundzüge der theoretischen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.

Reviewed By

Review John W. Dawson (2016) Review of "David Hilbert's Lectures on the Foundations of Arithmetic and Logic, 1917--1933". Historia Mathematica (pp. 105-107). unapi

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). unapi

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Authors & Contributors
Olga Hoppe-Kondrikova
Ciesielska, Danuta
Zach, Richard
Willea, Matthias
Verburgt, Lukas M.
Stillwell, John
Perspectives on Science
Historia Mathematica
Studia Historiae Scientiarum
Theoria (0495-4548)
Studies in History and Philosophy of Science
Revue d'Histoire des Mathématiques
Kluwer Academic
Raffaello Cortina Editore
Springer International
de Gruyter
Formalization (philosophy)
Philosophy of mathematics
Hilbert, David
Gödel, Kurt
Kant, Immanuel
Gauss, Carl Friedrich
Zermelo, Ernst
Tarski, Alfred
Time Periods
20th century, early
19th century
20th century
Cracow (Poland)
Paris (France)
Göttingen. Universität

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