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The own character of mathematics discussed with consideration of the proof of the four-color theorem

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Zusammenfassung

Der Beweis des Vierfarbensatzes mit Hilfe eines Computers, der so viel Zeit erforderte, daß ein Mensch die Berechnungen niemals überprüfen könnte, hat Zweifel erregt an vier philosophischen Annahmen über Mathematik. Die Mathematik ist die Lehre der Klassifikation, insoweit als sie vollständig abstrahiert von der Art der zu klassifizierenden Dinge. Diese Auffassung wird vom Beweis des Vierfarbensatzes nicht erschüttert. Wahrscheinlich kann mathematisches Denken nicht vor sich gehen ohne sinnliche Vorstellungen, aber die Eigenschaften mathematischer Gegenstände sind unabhängig von ihrer Weise sinnlicher Vorstellung.

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Authors and Affiliations

  1. SISWO Sektor Wissenschaft und Methode, Oudezijds Achterburgwal 128, 1012 DT, Amsterdam, Niederlande

    W. A. Verloren van Themaat

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  1. W. A. Verloren van Themaat
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I thank Dr. R. F. Geyer for correcting my English.

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Verloren van Themaat, W.A. The own character of mathematics discussed with consideration of the proof of the four-color theorem. Zeitschrift für Allgemeine Wissenschaftstheorie 20, 340–350 (1989). https://doi.org/10.1007/BF01801483

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