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Formen Der Anschauung by Pirmin Stekeler-Weithofer

Formen Der Anschauung

by Pirmin Stekeler-Weithofer
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Book cover type: Hardcover
  • ISBN13: 9783110194357
  • Binding: Hardcover
  • Subject: N/A
  • Publisher: de Gruyter
  • Publisher Imprint: de Gruyter
  • Publication Date:
  • Pages: 411
  • Original Price: USD 77.0
  • Language: German
  • Edition: N/A
  • Item Weight: 753 grams
  • BISAC Subject(s): History & Philosophy, Logic, and Language

Das Buch zeigt, inwiefern nicht, wie man üblicherweise sagt, die Arithmetik, Logik und Mengenlehre, sondern die Geometrie die Königin der Mathematik ist, weil nämlich die oft verpönte Anschauung allen ihren Axiomatisierungen und Anwendungen zugrunde liegt, und zwar in der Form eines diagrammtheoretischen Strukturmodells. Dessen Punkte, Geraden und Ebenen sind selbst immer schon raumlose Teilformen idealer Formen. Zu den 'reellen Zahlen' als reine Grö enproportionen gelangt man durch Ausweitung des Punktbereiches zunächst über den Fundamentalsatz der Algebra. Aber erst Cantors Naive Mengenlehre liefert genügend Nullstellen für beliebige stetige Funktionen. Dabei ist die euklidische Geometrie eine Theorie der Körperformen, während für jede Theorie des Raumes, in dem sich Körper bewegen, immer auch schon die Zeit mathematisiert werden muss, so dass der Bewegungsraum nie einfach 'dreidimensional' ist. Diese Unterscheidung zum Anschauungsraum geformter Körper macht das vierdimensionale Minkowski-Modell der Raum-Zeit in Einsteins spezieller Relativitätstheorie allererst voll begreifbar, zumal sich im empiristischen bzw. konventionalistischen Ansatz Reichenbachs, Grünbaums und vieler anderer Autoren deutliche Mängel finden.

Pirmin Stekeler-Weithofer, Universität Leipzig.

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