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Unvollständigkeit Und Unentscheidbarkeit: Die Metamathematischen Resultate Von Gödel, Church, Kleene, Rosser Und Ihre Erkenntnistheoretische Bedeutung

Unvollständigkeit Und Unentscheidbarkeit: Die Metamathematischen Resultate Von Gödel, Church, Kleene, Rosser Und Ihre Erkenntnistheoretische Bedeutung

          
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About the Book

Der heutige Erkenntnistheoretiker kann an den Resultaten der logischen und mathematischen Grundlagenforschung nicht mehr vorbei- gehen. Insbesondere sind viele der innerhalb der Metamathematik gewonnenen Ergebnisse von einer so auBerordentlichen theoretischen Bedeutung und Tragweite, daB deren genaues Studium fur jeden, der erkenntnistheoretische Untersuchungen betreiben will, welche auf der Hohe der Zeit stehen, ganz unerlii. J3lich ist. Durch jene Ergebnisse ge- winnen wir tiefste Einblicke in die Endlichkeit unseres Denkvermogens, in die Reichweite und die Grenzen des axiomatisch-deduktiven Vor- gehens, in das Verhaltnis zwischen formalen, kalkiilmaBig aufgebauten logischen sowie mathematischen Systemen und dem nichtformalisierten intuitiven SchlieBen, in die Beziehung zwischen logischer und mathe- matischer Wahrheit einerseits und Beweisbarkeit andererseits, in die Relation zwischen anfechtbaren, "bedenklichen" SchluBweisen der klassischen Logik und fur unbedenklich gehaltenen Operationen, durch welche die ersteren nachtraglich gerechtfertigt werden sollen. Bei ver- schiedenen dieser Resultate wird von Oberlegungen ausgegangen, die eine groBe Ahnlichkeit besitzen mit bereits von fruher her bekannten philosophischen Gedankengangen, insbesondere solchen, die zur Konstruk- tion von Paradoxien fiihrten. Diese Paradoxien waren meist als mehr oder weniger unfruchtbare, mehr oder weniger sophistische gedankliche Spielereien aufgefaBt worden. Nun konnten aber bedeutende metalogische und metamathematische Resultate dadurch gewonnen werden, daB man an jenen zu Paradoxien fiihrenden Oberlegungen gewisse Modifikationen vornahm, fehlerhafte Elemente ausschied und giiltige SchluBfolgerungen prazisierte und in geschickter Weise auswertete. Dies gilt insbesondere fiir die Antinomie des Liigners von EPIMEN'IDES und das Paradoxon von RICHARD.


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Product Details
  • ISBN-13: 9783211812082
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Edition: 0003-3., Verb. Aufl.
  • Language: German
  • Returnable: Y
  • Spine Width: 7 mm
  • Weight: 181 gr
  • ISBN-10: 3211812083
  • Publisher Date: 13 Dec 1973
  • Binding: Paperback
  • Height: 229 mm
  • No of Pages: 116
  • Series Title: German
  • Sub Title: Die Metamathematischen Resultate Von Gödel, Church, Kleene, Rosser Und Ihre Erkenntnistheoretische Bedeutung
  • Width: 152 mm


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Unvollständigkeit Und Unentscheidbarkeit: Die Metamathematischen Resultate Von Gödel, Church, Kleene, Rosser Und Ihre Erkenntnistheoretische Bedeutung
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