Document (#41087)

Author

Ortlieb, C.P.

Title

Heinrich Hertz und das Konzept des mathematischen Modells

Source

https://www.math.uni-hamburg.de/home/ortlieb/OrtliebHertzModell.pdf

Year

200x

Abstract

Die Einleitung zu Heinrich Hertz' letztem Werk "Die Prinzipien der Mechanik in neuem Zusammenhange dargestellt" ist ein Meilenstein auf dem langen Weg von Galileis Auffassung, das "Buch der Natur" sei in "geometrischen Zeichen geschrieben", zum modernen Konzept des mathematischen Modells. Hertz scheint der Erste gewesen zu sein, der die Bedeutung der naturwissenschaftlichen Entwicklung des 19. Jahrhunderts für die Rolle der Mathematik in der Naturerkenntnis ins Bewusstsein gehoben und die Konsequenzen deutlich ausgesprochen hat: Es gibt für einen Gegenstandsbereich etwa der Physik verschiedene richtige mathematische Beschreibungen und nicht nur die eine. Deswegen müssen für die Auswahl der "inneren Scheinbilder und Symbole der äußeren Gegenstände" (im heutigen Sprachgebrauch: der mathematischen Modelle) weitere Kriterien hinzu kommen. Hertz nennt als die drei wichtigsten: Richtigkeit, Zulässigkeit, Zweckmäßigkeit. Das damit verbundene Auseinanderfallen von Mathematik und Substanzwissenschaften hat Folgen auch für die Grenzen der Naturerkenntnis, die mehr als hundert Jahre später immer noch oft übersehen werden.

Content

Beitrag zur Tagung «Allgemeine Mathematik: Mathematik und Gesellschaft. Philosophische, historische und didaktische Perspektiven», Schloss Rauischholzhausen, 18. - 20. Juni 2015.

Field

Mathematik
Philosophie

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