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Die Antinomien

In: Briefe

Author

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  • Georg Cantor

Abstract

Zusammenfassung Die Cantorsche Mengenlehre wurde zu Beginn des 20. Jahrhunderts für viele Mathematiker und Philosophen suspekt, als Russell den Nachweis erbrachte, daß man auf in sich widerspruchsvolle (nicht „konsistente“) Mengen stößt, wenn man den Cantorschen Mengenbegriff in uneingeschränkter Allgemeinheit anwendet. Hier kann die Beschäftigung mit Cantors Korrespondenz zu der Erkenntnis verhelfen, daß Cantor selbst schon Jahre zuvor die Möglichkeit solcher Antinomienbildung erkannt hatte. Wir wissen das aus seiner Korrespondenz mit Hilbert aus den Jahren 1897 und 1898. Der Schöpfer der Mengenlehre argumentiert, daß er ja immer verlangt habe, daß die Mengen „wohl definiert“ sein müssen. Und in sich widerspruchsvolle Mengen sind eben nicht wohldefiniert. Später hat er noch hinzugefügt, daß die Mengen auch „fertig“ sein müssen.

Suggested Citation

  • Georg Cantor, 1991. "Die Antinomien," Springer Books, in: Herbert Meschkowski & Winfried Nilson (ed.), Briefe, chapter 5, pages 8-10, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-74344-3_5
    DOI: 10.1007/978-3-642-74344-3_5
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