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Die vier Wissenschaften der Pythagoreer. Hundert Jahre formale Logik

Die vier Wissenschaften der Pythagoreer. Hundert Jahre formale Logik

Bartel L. ˜van derœ Waerden

84,75 €
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Editorial:
Springer Nature B.V.
Año de edición:
1977
Materia
Filosofía occidental: antigua, hasta c. 500
ISBN:
9783531082684
84,75 €
IVA incluido
Disponible

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Sobre IBD

Formal logic presupposes a formal language. A rudimentary formal language was given by G. Boole. A formal language which was sufficient for the purpose of mathematics was constructed by Gottlob Frege in his book ' Begriffsschrift, eine der arithmetischen nachgebildete Formel­ sprache des reinen Denkens' (1879). Since that time we have an abun­ dant spectrum of logics based on formal languages. There are applications mainly in mathematics ('metamathematics'), but also e. g. in philos­ ophy, linguistics and computer science. The most important formal language is the first order predicate calculus. There has been a gradual emancipation of this language via the theory of types given by Bertrand Russell. This paper discusses that development in some details. Diskussion Herr Hlawka: Sie haben gesagt, der Wiener Kreis sei tiber Carnap von Frege beeinfluBt gewesen. Ich wtirde eher meinen, tiber Russell. Dann haben Sie gesagt, daB bei Frege der Funktionsbegriff im Vorder­ grund steht. Ich finde, daB dieser Gesichtspunkt gerade in der von Neu­ mannschen Theorie verwirklicht ist. Herr Hermes: Von Neumann hat in der Tat den Funktionsbegriff als Grundbegriff der Mengenlehre gewahlt. Es hat aber niemand direkt dar­ an angekntipft. Herr Hlawka: Vielleicht die moderne Kategorientheorie. Herr Hermes: Das stimmt. Herr Hlawka: Aber dann ist es doch so, daB der Pradikatenkalktil der ersten Stufe nur dann ausreicht, die klassische Mathematik zu begrtin­ den, das heiBt kurz das, was bei Bourbaki steht, wenn man die Mengen­ lehre als Fundament nimmt.

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