Archive for History of Exact Sciences

, Volume 71, Issue 3, pp 245–278

Searches for the origins of the epistemological concept of model in mathematics

Article
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Abstract

When did the concept of model begin to be used in mathematics? This question appears at first somewhat surprising since “model” is such a standard term now in the discourse on mathematics and “modelling” such a standard activity that it seems to be well established since long. The paper shows that the term— in the intended epistemological meaning—emerged rather recently and tries to reveal in which mathematical contexts it became established. The paper discusses various layers of argumentations and reflections in order to unravel and reach the pertinent kernel of the issue. The specific points of this paper are the difference in the epistemological concept to the usually discussed notions of model and the difference between conceptions implied in mathematical practices and their becoming conscious in proper reflections of mathematicians.

Mathematics Subject Classification

00A30 01A55 01A60 01A90 51-03 

Zusammenfassung

Wann begann der Begriff des Modells in der Mathematik benutzt zu werden? Diese Frage mag auf den ersten Blick Erstaunen auslösen, weil ,Modell’ heute im Diskurs über die Mathematik einen solch selbstverständlichen Ausdruck und ,Modellieren’ eine solche Standard-Aktivität bildet, dass man ihn als Begriff für schon lange etabliert hält. Der Artikel zeigt, dass dessen Ursprünge—in der hier intendierten epistemologischen Bedeutung—dagegen relativ jung sind und versucht, die mathematischen Kontexte aufzudecken, in denen der Begriff etabliert wurde. Der Artikel führt durch mehrere Schichten von Argumentationen und Reflexionen, um den tatsächlichen Kern der Fragestellung herauszuschälen und ihn so zu erreichen. Der spezifische Ansatz des Artikels betrifft den Unterschied zwischen der epistemologischen Bedeutung von Modell zum üblichen Verständnis von Modell sowie den Unterschied zwischen in mathematischen Praktiken implizierten Konzeptionen und dem Bewusstwerden in eigenen Reflexionen von Mathematikern.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.IDM, Fakultät für MathematikUniversität BielefeldBielefeldFederal Republic of Germany

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