PL EN


Journal
2012 | 20 | 3(79) | 99-109
Article title

Arytmetyka u początku abstrakcyjnego pojmowania geometrii przez Hilberta

Title variants
EN
ARITHMETIC AT THE ORIGIN OF HILBERT’S ABSTRACT CONCEPTION OF GEOMETRY
Languages of publication
PL
Abstracts
EN
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.
Journal
Year
Volume
20
Issue
Pages
99-109
Physical description
Contributors
  • Uniwersytet Papieski Jana Pawła II w Krakowie, Wydział Filozoficzny, ul. Kanonicza 9, 31-002 Kraków, Poland., dada59@poczta.onet.pl
References
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.cejsh-bb97a588-c1b8-431e-a9db-ed280f308ac8
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