Philosophy Lexicon of Arguments

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A. d'Abro Die Kontroversen über das Wesen der Mathematik 1939 in Kursbuch 8 Mathematik 1967

System/d'Abro: If we replace one postulate by another, we obtain a new postulate system, for which the Euclidean model is no longer valid. It may be that this model is verified by a new geometry or model.
Hilbert has e.g. shown that if the parallel postulate is replaced by a suitably chosen one, the new postulate system is verified by Lobachevski's geometry.
In this case nothing new was discovered, since this geometry was already known. A completely new geometry, on the other hand, was secured when Hilbert rejected the Archimedean axiom.
d’Abro, A.

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Ed. Martin Schulz, access date 2017-05-26