New Foundations

New Foundations

New Foundations (NF) ist der Name einer axiomatischen Mengenlehre von Willard Van Orman Quine, benannt nach dessen Aufsatz New Foundations for Mathematical Logic (Neue Grundlagen der mathematischen Logik) von 1937. NF tendiert in mancher Hinsicht zur Typentheorie und unterscheidet sich von der Zermelo-Fraenkel-Mengenlehre in vielen Punkten, zum Beispiel gilt das Auswahlaxiom nicht und man kann auch die Existenz der Menge der natürlichen Zahlen nicht beweisen. Der NF-Mengenbegriff weicht also stark ab vom eingebürgerten Mengenbegriff. NF ist eher eine Theorie real existenter Klassen, in der der übliche Mengenbegriff nicht vorkommt.

Literatur

  • Quine, Willard Van Orman: New Foundations for Mathematical Logic , in: Am. Math. Monthly 44 (1937), S. 70-80.
  • Quine, Willard Van Orman: From a logical Point of view. 9 logico-philosophical essays, Harvard U.P., Cambridge, Mass. 1953, S. 80-101.

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