Arytmetyka u początku abstrakcyjnego pojmowania geometrii przez Hilberta

Filozofia Nauki 20 (3) (2012)
  Copy   BIBTEX

Abstract

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 di-rect source of the change was having heard a lecture by Wiener on projective geome-try. 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, pre-sented 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

Other Versions

No versions found

Links

PhilArchive

    This entry is not archived by us. If you are the author and have permission from the publisher, we recommend that you archive it. Many publishers automatically grant permission to authors to archive pre-prints. By uploading a copy of your work, you will enable us to better index it, making it easier to find.

    Upload a copy of this work     Papers currently archived: 102,217

External links

  • This entry has no external links. Add one.
Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

On Tait on Kant and Finitism.W. Sieg - 2016 - Journal of Philosophy 113 (5/6):274-285.
Hilbert, completeness and geometry.Giorgio Venturi - 2011 - Rivista Italiana di Filosofia Analitica Junior 2 (2):80-102.
On a Geometric Foundation of Mathematics.Giuseppina Anatriello - 2017 - Science and Philosophy 5 (1):91-108.
Dedekind and Wolffian Deductive Method.José Ferreirós & Abel Lassalle-Casanave - 2022 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 53 (4):345-365.
Ideal Elements in Hilbert's Geometry.John Stillwell - 2014 - Perspectives on Science 22 (1):35-55.
Kant and Finitism.W. W. Tait - 2016 - Journal of Philosophy 113 (5/6):261-273.

Analytics

Added to PP
2013-03-14

Downloads
0

6 months
0

Historical graph of downloads

Sorry, there are not enough data points to plot this chart.
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references