Article ID: CBB001213913

On Hilbert's Axiomatics of Propositional Logic (2014)


Abrusci, V. Michele (Author)

Perspectives on Science
Volume: 22, no. 1
Issue: 1
Pages: 115-132

Publication Date: 2014
Edition Details: Part of a special issue, “Hilbert's Axiomatics---Geometry, Physics, Logic”
Language: English

In this paper I will consider the axioms for propositional logic which were presented by Hilbert in his conferences during the year 1922, and those which were presented by Hilbert and Bernays in the book Grundlagen der Mathematik, I (1934). I will describe a general procedure in order to translate Hilbert's axioms into rules on sequents and I will show that, following this procedure, Hilbert's axioms become particular cases of (derived or primitive) rules of Gentzen's Sequent Calculus and contain ideas which will be focused and developed in Gentzen's Sequent Calculus and also in more recent logical investigations.

Included in

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

Citation URI

Similar Citations

Article Sieg, Wilfried; (2014)
The Ways of Hilbert's Axiomatics: Structural and Formal (/isis/citation/CBB001213914/)

Article Rédei, Miklós; (2014)
Hilbert's 6th Problem and Axiomatic Quantum Field Theory (/isis/citation/CBB001213911/)

Article Stillwell, John; (2014)
Ideal Elements in Hilbert's Geometry (/isis/citation/CBB001213909/)

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 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/)

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/)

Article Cassou-Noguès, Pierre; (2006)
Signs, Figures and Time: Cavaillès on “Intuition” in Mathematics (/isis/citation/CBB000933621/)

Article Karela, Catherine; (2010)
Hilbert on Different Notions of Completeness: A Conceptual and Historical Analysis (/isis/citation/CBB001220619/)

Chapter David E. Rowe; (2015)
Historical Events in the Background of Hilbert’s Seventh Paris Problem (/isis/citation/CBB995513838/)

Authors & Contributors
Majer, Ulrich
Sieg, Wilfried
Gauthier, Yvon
Di, Li
Corry, Leo
Cerroni, Cinzia
Perspectives on Science
Nei Menggu Shifan Daxue Xuebao (Ziran Kexue Ban)
Revue d'Histoire des Mathématiques
Theoria (0495-4548)
Archive for History of Exact Sciences
Studies in History and Philosophy of Science
Kluwer Academic
de Gruyter
Raffaello Cortina Editore
Springer International
Formalization (philosophy)
Philosophy of mathematics
Hilbert, David
Gödel, Kurt
Kant, Immanuel
Kronecker, Leopold
Dedekind, Richard
Gauss, Carl Friedrich
Time Periods
20th century, early
19th century
20th century
Paris (France)
Göttingen. Universität

Be the first to comment!

{{ comment.created_by.username }} on {{ comment.created_on | date:'medium' }}

Log in or register to comment