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
Mechthild Koreuber
Nobrega, Hugo
Viana, Petrucio
Cerioli, Márcia R.
Silveira, Guilherme
Concepts
Mathematics
Logic
Philosophy of mathematics
Algebra
Infinitesimals
Philosophy
Time Periods
19th century
20th century, early
18th century
Places
Germany
Great Britain
England
United States
Institutions
Cambridge University
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