Article ID: CBB001211472

On the Creative Role of Axiomatics. The Discovery of Lattices by Schröder, Dedekind, Birkhoff, and Others (2011)

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Schlimm, Dirk (Author)


Synthese
Volume: 183, no. 1
Issue: 1
Pages: 47-68


Publication Date: 2011
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.

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Citation URI
https://data.isiscb.org/isis/citation/CBB001211472/

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Authors & Contributors
Peckhaus, Volker
Grattan-Guinness, Ivor
Luciano, Erika
Gray, Jeremy
Dea, Shannon
Campos, Daniel G.
Journals
Revue d'Histoire des Mathématiques
Transactions of the Charles S. Peirce Society
History and Philosophy of Logic
Archive for History of Exact Sciences
Journal of Dialectics of Nature
Foundations of Science
Publishers
Princeton University Press
Vittorio Klostermann
Indiana University
Mathematical Association of America
Concepts
Mathematics
Logic
Philosophy of mathematics
Algebra
Philosophy
Infinitesimals
People
Dedekind, Richard
Peirce, Charles Sanders
Cantor, Georg Ferdinand Ludwig
Peano, Giuseppe
Poincaré, Jules Henri
Birkhoff, George David
Time Periods
19th century
20th century, early
18th century
Places
Germany
Great Britain
England
United States
Institutions
Cambridge University
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