David Hilbert's Lectures on the Foundations of Mathematics and Physics - 2: David Hilbert's Lectures on the Foundations of Arithmetic and Logic, 1894-1917

Volume 2 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).

About the author

David Hilbert (1862-1943) gilt als der vielleicht universellste Mathematiker des ausgehenden 19. und beginnenden 20. Jahrhunderts. Er hat auf zahlreichen Gebieten der Mathematik und der mathematischen Physik grundlegende neue Resultate vorgelegt und wesentliche Entwicklungen angebahnt.

Summary

Volume 2 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).

Product details

• Authors: David Hilbert
• Assisted by: William Ewald (Editor), Michae Hallett (Editor), Michael Hallett (Editor), Ulrich Majer (Editor), Ulrich Majer et al (Editor), Wilfried Sieg (Editor)
• Publisher: Springer, Berlin
• Languages: German
• Product format: Hardback
• Release: 14.11.2026
• EAN: 9783540206057
• ISBN: 978-3-540-20605-7
• No. of pages: 690
• Illustrations: Etwa 690 S.
• Sets: David Hilbert's Lectures on the Foundations of Mathematics and Physics; David Hilbert's Lectures on the Foundations of Mathematics and Physics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > General, dictionaries; Logic, mathematische Grundlagen, Mathematik: Logik, Hilbert, geometry, arithmetic, Foundation, Physics, History of Mathematical Sciences, Mathematical Logic and Foundations, MSC (2000): 01A55, 01A60, 01A75, 03-03, 51-03, 70-03, 70A05,