====== Menge ======

von [[autoren:nachname_vorname|Vorname Nachname]]

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^ lat.    |      |^Synonyme        |      |
^ engl.   |      |^Gegenbegriffe   | |
^ franz.  |    |^Unterbegriffe   | |
^ Wortfeld| ||||

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===== Disziplinäre Begriffe =====

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===== Material =====

==== A. Primärmaterial ====

|**1739**|Zedler, Johann Heinrich: (Art.) [[http://mdz10.bib-bvb.de/~zedler/zedler2007/blaettern/einzelseite.html?id=184105&bandnummer=20&seitenzahl=0351&supplement=0&dateiformat=1|Menge]], in: Grosses vollständiges Universal Lexicon aller Wissenschafften und Künste, Bd. 20, S. 351-352.|

==== B. Sekundärmaterial ====
=== Begriffsgeschichtliche Arbeiten ===

  * Steiner, H. G.: (Art.) Mengenlehre, in: Historisches Wörterbuch der Philosophie. Hg.v. J. Ritter u. K. Gründer. Bd. 5, Basel/Stuttgart, 1980, Sp. 1044 - 1059.

=== Sonstige Literatur ===

  * Felscher, Walter: Naive Mengen und abstrakte Zahlen. 3 Bde. Mannheim: Bibliographische Wiss. Verlag; Repr. 1989  1978/1979.

  * Muller, F.A.: Sets, Classes, and Categories. The British Journal for the Philosophie of Science 52, 2001, S. 539-573.

|Abstract: This paper, accessible for a general philosophical audience having only some fleeting acquaintance with set-theory and category-theory, concerns the philosophy of mathematics, specifically the bearing of category-theory on the foundations of mathematics. We argue for six claims. (I) A founding theory for category-theory based on the primitive concept of a set or a class is worthwile to pursue. (II) The extant set-theoretical founding theories for category-theory are conceptually flawed. (III) The conceptual distinction between a set and a class can be seen to be formally codified in Ackermann's axiomatisation of set-theory. (IV) A slight but significant deductive extension of Ackermann's theory of sets and classes founds Cantorian set-theory as well as category-theory, and therefore can pass as a founding theory of the whole of mathematics. (V) The extended theory does not suffer from the conceptual flaws of the extant set-theoretical founding theories. (VI) The extended theory is not only conceptually but also logically superior to the competing set-theories because its consistency can be proved on the basis of weaker assumptions than the consistency of the competition.|

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