Sieg, Wilfried (Author)

Perspectives on Science

Volume: 22, no. 1

Issue: 1

Pages: 133-157

Publication Date: 2014

Edition Details: Part of a special issue, “Hilbert's Axiomatics---Geometry, Physics, Logic”

Language: English

Edition Details: Part of a special issue, “Hilbert's Axiomatics---Geometry, Physics, Logic”

Language: English

It is a remarkable fact that Hilbert's programmatic papers from the 1920s still shape, almost exclusively, the standard contemporary perspective of his views concerning (the foundations of) mathematics; even his own, quite different work on the foundations of geometry and arithmetic from the late 1890s is often understood from that vantage point. My essay pursues one main goal, namely, to contrast Hilbert's formal axiomatic method from the early 1920s with his existential axiomatic approach from the 1890s. Such a contrast illuminates the circuitous beginnings of the finitist consistency program and connects the complex emergence of existential axiomatics with transformations in mathematics and philosophy during the 19th century; the sheer complexity and methodological difficulties of the latter development are partially reflected in the well known, but not well understood correspondence between Frege and Hilbert. Taking seriously the goal of formalizing mathematics in an effective logical framework leads also to contemporary tasks, not just historical and systematic insights; those are briefly described as one direction for fascinating work.

...More
Included in

Article
Lupacchini, Rossella
(2014)
Hilbert's Axiomatics as “Symbolic Form”?.
*Perspectives on Science*
(pp. 1-34).

Citation URI

Article
Abrusci, V. Michele;
(2014)

On Hilbert's Axiomatics of Propositional Logic
(/isis/citation/CBB001213913/)

Article
Stillwell, John;
(2014)

Ideal Elements in Hilbert's Geometry
(/isis/citation/CBB001213909/)

Article
Rédei, Miklós;
(2014)

Hilbert's 6th Problem and Axiomatic Quantum Field Theory
(/isis/citation/CBB001213911/)

Article
Majer, Ulrich;
(2014)

The “Axiomatic Method” and Its *Constitutive Role* in Physics
(/isis/citation/CBB001213910/)

Book
Gabriele Lolli;
(2016)

Tavoli, sedie, boccali di birra: David Hilbert e la matematica del Novecento
(/isis/citation/CBB100106060/)

Book
Gauthier, Yvon;
(2002)

Internal Logic: Foundations of Mathematics from Kronecker to Hilbert
(/isis/citation/CBB000301820/)

Book
Hilbert, David;
Ewald, William;
Sieg, Wilfried;
Hallett, Michael;
Majer, Ulrich;
Schlimm, Dirk;
(2013)

David Hilbert's Lectures on the Foundations of Arithmetic and Logic, 1917--1933
(/isis/citation/CBB001551530/)

Article
Lupacchini, Rossella;
(2014)

Hilbert's Axiomatics as “Symbolic Form”?
(/isis/citation/CBB001213908/)

Article
Cerroni, Cinzia;
(2007)

The Contributions of Hilbert and Dehn to Non-Archimedean Geometries and Their Impact on the Italian School
(/isis/citation/CBB000930656/)

Chapter
Corry, Leo;
(2006)

Axiomatics, Empiricism, and *Anschauung* in Hilbert's Conception of Geometry: Between Arithmetic and General Relativity
(/isis/citation/CBB000800120/)

Book
Elena Anne Corie Marchisotto;
Francisco Rodriguez-Consuegra;
James T. Smith;
(2021)

The Legacy of Mario Pieri in Foundations and Philosophy of Mathematics
(/isis/citation/CBB763111584/)

Book
Gandon, Sébastien;
(2012)

Russell's Unknown Logicism: A Study in the History and Philosophy of Mathematics
(/isis/citation/CBB001201203/)

Book
Linsky, Bernard;
(2011)

The Evolution of *Principia Mathematica*: Bertrand Russell's Manuscripts and Notes for the Second Edition
(/isis/citation/CBB001221112/)

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
Reich, Karin;
(2008)

Der Desarguessche und der Pascalsche Satz: Hessenbergs Beitrag zu Hilberts Grundlagen der Geometrie
(/isis/citation/CBB000950185/)

Chapter
Mancosu, Paolo;
Zach, Richard;
Badesa, Calixto;
(2009)

The Development of Mathematical Logic from Russell to Tarski, 1900--1935
(/isis/citation/CBB001210349/)

Article
Pejlare, Johanna;
(2007)

Torsten Brodén's Work on the Foundations of Euclidean Geometry
(/isis/citation/CBB000773211/)

Chapter
Hallett, Michael;
(2010)

Frege and Hilbert
(/isis/citation/CBB001211657/)

Be the first to comment!