Arytmetyka u początku abstrakcyjnego pojmowania geometrii przez Hilberta
ARITHMETIC AT THE ORIGIN OF HILBERT’S ABSTRACT CONCEPTION OF GEOMETRY
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In 1891, Hilbert came to the conclusion that geometry is not a science of the physical space but is an abstract science. Hilbert’s new position was repeated in the introduction to Grundlagen der Geometrie in 1899. The aim of this paper is to show the sources of change of Hilbert’s position in 1891. We showed that the direct source of the change was having heard a lecture by Wiener on projective geometry. Wiener presented there a project of geometry as a science of abstract objects i.e. objects as sets of minimal number of – only relational – properties. We showed that this idea was derived by Wiener from Dedekind’s arithmetic of natural numbers, presented in 1888 in Was sind und was sollen die Zahlen? Thus – and this is the essential thesis of our paper – the original source of Hilbert’s idea of geometry as a abstract science is included in Dedekind’s concept of arithmetic.
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