Between 1897 and 1902, there took place a brief correspondence between Frege and Hilbert, consisting of four letters from Frege, and two letters and three postcards from Hilbert. It centres on Frege's reactions to Hilbert's classic Grundlagen der Geometrie, first published in 1899, and Hilbert's restatements in his letters to Frege of the foundational positions which that work, sometimes only implicitly, embodies. Despite the obvious richness of common purpose between Frege and Hilbert, the correspondence is especially instructive because of the strong disagreements expressed. For example, the two disagreed on the form and function of definitions, the nature, purpose and formulation of axioms, the nature of (axiomatized) mathematical theories, the method of independence proofs in geometry, the role and form of consistency proofs and the nature of mathematical existence. Many of the articles of disagreement, especially those on axioms and independence proofs, also reveal or underline significant differences in their respective conceptions of logic. Frege followed the correspondence with two polemical, and wider-ranging, articles on similar or related themes, Hilbert himself having apparently declined Frege's suggestion that their exchange of views be published. These two papers help to fill out the picture on Frege's side, first by restating Frege's opposition, and then by presenting his insights into the formal structure of Hilbert's position. Especially important are Frege's attempts in his second article to render central results of Hilbert's project as read through his own system.
...MoreBook Ricketts, Tom; Potter, Michael D. (2010) The Cambridge Companion to Frege.
Article
Stillwell, John;
(2014)
Ideal Elements in Hilbert's Geometry
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Chapter
Corry, Leo;
(2006)
Axiomatics, Empiricism, and Anschauung in Hilbert's Conception of Geometry: Between Arithmetic and General Relativity
(/isis/citation/CBB000800120/)
Article
Demopoulos, William;
(1994)
Frege, Hilbert, and the conceptual structure of model theory
(/isis/citation/CBB000049624/)
Article
Pedro J. Freitas;
(2019)
The Correspondence from Ernesto Cesàro to Francisco Gomes Teixeira
(/isis/citation/CBB711366439/)
Chapter
Mancosu, Paolo;
Zach, Richard;
Badesa, Calixto;
(2009)
The Development of Mathematical Logic from Russell to Tarski, 1900--1935
(/isis/citation/CBB001210349/)
Chapter
Weiner, Joan;
(2010)
Understanding Frege's Project
(/isis/citation/CBB001211648/)
Chapter
Thiel, Christian;
(2009)
Gottlob Frege and the Interplay between Logic and Mathematics
(/isis/citation/CBB001210345/)
Book
Schüler, Wolfgang;
(1983)
Grundlegungen der Mathematik in transzendentaler Kritik: Frege und Hilbert
(/isis/citation/CBB000007451/)
Article
Schüler, Wolfgang;
(1984)
Überlegung zu den Grundlegungsversuchen der Mathematik von Frege und Hilbert vom Standpunkt der Transzendentalphilosophie aus
(/isis/citation/CBB000016610/)
Article
Wehmeier, Kai F.;
(1997)
Aspekte der Frege--Hilbert--Korrespondenz
(/isis/citation/CBB000079357/)
Chapter
Wilson, Mark;
(2010)
Frege's Mathematical Setting
(/isis/citation/CBB001211656/)
Article
Sieg, Wilfried;
(2014)
The Ways of Hilbert's Axiomatics: Structural and Formal
(/isis/citation/CBB001213914/)
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
Sommer, Klaus P.;
(2005)
In das Deutschland “von Hilbert und Einstein”. Briefe von Einstein, Planck, Nernst, Debye, Born, Sommerfeld, Courant, Ehrenfest, Weyl und Althoff an David Hilbert, gefunden auf einem Göttinger Dachboden
(/isis/citation/CBB000670823/)
Chapter
Toepell, M.-M.;
(1985)
Zur Schlüsselrolle Friedrich Schurs bei der Entstehung von David Hilberts Grundlagen der Geometrie
(/isis/citation/CBB000050113/)
Chapter
Reich, Karin;
(2008)
Der Desarguessche und der Pascalsche Satz: Hessenbergs Beitrag zu Hilberts Grundlagen der Geometrie
(/isis/citation/CBB000950185/)
Article
Ausejo Martínez, Elena;
Ausejo Lifante, Elena;
(2017)
Correspondencia de Zoel García de Galdeano con matemáticos alemanes: Georg Cantor
(/isis/citation/CBB631684117/)
Chapter
Netz, Reviel;
(2012)
The Texture of Archimedes' Writings: Through Heiberg's Veil
(/isis/citation/CBB001320141/)
Chapter
Vitrac, Bernard;
(2012)
The Euclidean Ideal of Proof in The Elements and Philological Uncertainties of Heiberg's Edition of the Text
(/isis/citation/CBB001320139/)
Article
Günther Eder;
(2021)
Frege on intuition and objecthood in projective geometry
(/isis/citation/CBB221284966/)
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