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Metamathematik Der Elementarmathematik by E. Engeler

Metamathematik Der Elementarmathematik

by E. Engeler
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Book cover type: Paperback
  • ISBN13: 9783540121510
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 134
  • Original Price: EUR 51.39
  • Language: German
  • Edition: N/A
  • Item Weight: 241 grams
  • BISAC Subject(s): Logic

Dieses Buch ist kein Lehrbuch. Doch ist es aus Vorlesungen gewachsen, die ich seit ein paar Jahren an der ETH in ZUrich gehalten habe. Es wendet sich an Studenten der Mathematik mittlerer und oberer Semester, aber weniger mit dem Ziel, diesen mathematische Logik oder Axiomatik beizubringen, als vielmehr, urn in ihnen die kritischen Fahigkeiten gegenUber der Mathematik zu wecken und zu scharfen. Denn nur allzu leicht wird der Student durch un sere Erziehung eingelullt. Die jahre- lange Beschaftigung mit der Technik der Schulalgebra und -geometrie und mit dem irnrnensen Gebaude der Analysis lasst bei fast allen das GefUhl aufkornrnen, sie wUssten nun, was die reel len Zahlen seien, was eine Funktion, was der euklidische Raum, was eine Rechenvorschrift sei. Es liegt mir fern, die NUtzlichkeit, ja Notwendigkeit, eines weit- gehenden Konsensus in der Mathematik zu verneinen. Wogegen ich aber ankarnpfe, ist die Phantasielosigkeit, die in der Tendenz liegt, Grundbegriffe und Grundhaltungen unbesehen zu Ubernehrnen. Was ich in diesem BUchlein darstellen will, ist die systematische Kritik an den Grundlagen der Mathematik, welche die mathematische Logik des 20. Jahrhunderts technisch moglich gemacht hat. Der Terminus "Meta- mathematik" unseres Titels deutet also auf die Methode, "Elementar- mathematik" weist auf den Gegenstand: Analysis, Geometrie und Algo- rithrnik. In nuce: Wie kornrnt man zu den Axiomen der Elementarmathematik, und was ist von ihnen zu halten? Die Fertigstellung dieses BUchleins verdanke ich der kompetenten Arbeit von Brigitte Knecht (Text) und Dr. Ernst Graf (Zeichnungen).

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