Die Eindeutigkeit der konstruktiven Geometrie (original) (raw)
1987, Journal for General Philosophy of Science - Zeitschrift für Allgemeine Wissenschaftstheorie
Inquiries of Wellstein, Griinbaum and others have proved that there are indefinitely many different spatial models of Euklidian geometry. The points, lines and planes of these models are related to each other as the points, straight lines and planes of Euklidian geometry, but they are obviously totally different from them. That means that the axiomatic Euklidian geometry does not clearly determine the spatial forms of their planes and straight lines. The constructive geometry basing on approaches of Hugo Dingler tries to solve this problem of disambiguity so that a clear realization of the geometrical basic objects plane, straight line and rectangle and others is possible because of certain rules. On the one hand these rules are to pledge the techniques of realisation and on the other hand they are the basic for the deduction of statements on the technically realized geometrical basic objects. The rules are especially to pledge the selection of apt material that keep its form. The following will show that the disambiguity cannot be pledged by the mere laws established by the constructive geometry and especially that the problem of electing the material cannot be solved by these laws. Furthermore it proves to be necessary to analyze and reconstruct more circumstances describing the selection of apt material which exceed the present standard of constructive geometry.
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