On the Creative Role of Axiomatics. The Discovery of Lattices by Schröder, Dedekind, Birkhoff, and Others (2011)
Schlimm, Dirk (Author)
Synthese
Volume: 183, no. 1
Issue: 1
Pages: 47-68
Edition Details: Part of a special issue, “The Classical Model of Science II: The Axiomatic Method, the Order of Concepts and the Hierarchy of Sciences”
Language: English
Three different ways in which systems of axioms can contribute to the discovery of new notions are presented and they are illustrated by the various ways in which lattices have been introduced in mathematics by Schröder et al. These historical episodes reveal that the axiomatic method is not only a way of systematizing our knowledge, but that it can also be used as a fruitful tool for discovering and introducing new mathematical notions. Looked at it from this perspective, the creative aspect of axiomatics for mathematical practice is brought to the fore.
...MoreSimilar Citations
Article
Reck, Erich H.;
(2013)
Frege, Dedekind, and the Origins of Logicism
(/isis/citation/CBB001212886/)
Book
Steve Batterson;
(2017)
American Mathematics 1890-1913: Catching up to Europe
(/isis/citation/CBB996384427/)
Article
Mechthild Koreuber;
(2015)
Zur Einführung einer begrifflichen Perspektive in die Mathematik: Dedekind, Noether, van der Waerden
(/isis/citation/CBB619659341/)
Thesis
Keele, Lisa;
(2008)
Theories of Continuity and Infinitesimals: Four Philosophers of the Nineteenth Century
(/isis/citation/CBB001560801/)
Article
Peckhaus, Volker;
(2014)
Ernst Schröder on pasigraphy
(/isis/citation/CBB001551987/)
Article
Błaszczyk, Piotr;
Katz, Mikhail G.;
Sherry, David;
(2013)
Ten Misconceptions from the History of Analysis and Their Debunking
(/isis/citation/CBB001252715/)
Article
Emmylou Haffner;
(2019)
From Modules to Lattices: Insight into the Genesis of Dedekind's Dualgruppen
(/isis/citation/CBB728342102/)
Book
Gray, Jeremy;
(2008)
Plato's Ghost: The Modernist Transformation of Mathematics
(/isis/citation/CBB000950298/)
Chapter
Peckhaus, Volker;
(2009)
The Mathematical Origins of Nineteenth-Century Algebra of Logic
(/isis/citation/CBB001210344/)
Article
Roque, Tatiana;
(2011)
Stability of Trajectories from Poincaré to Birkhoff: Approaching a Qualitative Definition
(/isis/citation/CBB001034292/)
Thesis
David E. Dunning;
(2020)
Writing the Rules of Reason: Notations in Mathematical Logic, 1847–1937
(/isis/citation/CBB517005733/)
Book
Grattan-Guinness, I.;
(2000)
The Search for Mathematical Roots, 1870-1940: Logics, Set Theories and the Foundations of Mathematics from Cantor through Russell to Gödel
(/isis/citation/CBB000111675/)
Book
Ricketts, Tom;
Potter, Michael D.;
(2010)
The Cambridge Companion to Frege
(/isis/citation/CBB001211647/)
Article
David E. Dunning;
(2021)
The Logician in the Archive: John Venn’s Diagrams and Victorian Historical Thinking
(/isis/citation/CBB413337671/)
Book
Grattan-Guiness, I.;
(2000)
Search for Mathematical Roots, 1870-1940: Logics, Set Theories and the Foundations of Mathematics from Cantor Through Russell to Gödel
(/isis/citation/CBB000102346/)
Book
Jan Von Plato;
(2017)
The Great Formal Machinery Works: Theories of Deduction and Computation at the Origins of the Digital Age
(/isis/citation/CBB573478690/)
Article
Márcia R. Cerioli;
Hugo Nobrega;
Guilherme Silveira;
Petrucio Viana;
(2022)
On the (In)Dependence of the Peano Axioms for Natural Numbers
(/isis/citation/CBB173126247/)
Article
Despeaux, Sloan Evans;
(2014)
Questions/ réponses dans les périodiques britanniques des XVIIIe et XIXe siècles: un genre éditorial à la croisée de deux pratiques mathématiques
(/isis/citation/CBB001451430/)
Book
Künne, Wolfgang;
(2010)
Die Philosophische Logik Gottlob Freges: ein Kommentar; mit den Texten des Vorworts zu Grundgesetze der Arithmetik und der Logischen Untersuchungen I--IV
(/isis/citation/CBB001210615/)
Article
Luciano, Erika;
(2006)
At the Origins of Functional Analysis: G. Peano and M. Gramegna on Ordinary Differential Equations
(/isis/citation/CBB000770911/)
Be the first to comment!