Axiomathes 28 (2):155-180 (2018)

Boris Culina
University of Applied Sciences Velika Gorica, Croatia
In this article I develop an elementary system of axioms for Euclidean geometry. On one hand, the system is based on the symmetry principles which express our a priori ignorant approach to space: all places are the same to us, all directions are the same to us and all units of length we use to create geometric figures are the same to us. On the other hand, through the process of algebraic simplification, this system of axioms directly provides the Weyl’s system of axioms for Euclidean geometry. The system of axioms, together with its a priori interpretation, offers new views to philosophy and pedagogy of mathematics: it supports the thesis that Euclidean geometry is a priori, it supports the thesis that in modern mathematics the Weyl’s system of axioms is dominant to the Euclid’s system because it reflects the a priori underlying symmetries, it gives a new and promising approach to learn geometry which, through the Weyl’s system of axioms, leads from the essential geometric symmetry principles of the mathematical nature directly to modern mathematics.
Keywords Weyl’s axioms for Eucliedean geometry  A priority of Euclidean geometry  Philosophy of geometry  Elementary axioms for Euclidean geometry  Symmetries of Euclidean geometry
Categories (categorize this paper)
DOI 10.1007/s10516-017-9358-y
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

 PhilArchive page | Other versions
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Tarski's System of Geometry.Alfred Tarski & Steven Givant - 1999 - Bulletin of Symbolic Logic 5 (2):175-214.
Kant's Views on Non-Euclidean Geometry.Michael Cuffaro - 2012 - Proceedings of the Canadian Society for History and Philosophy of Mathematics 25:42-54.
Frege’s Philosophy of Geometry.Matthias Schirn - 2019 - Synthese 196 (3):929-971.
Thomas Reid’s Geometry of Visibles and the Parallel Postulate.Giovanni B. Grandi - 2005 - Studies in History and Philosophy of Science Part A 36 (1):79-103.
La geometria eterna. Nelson e le geometrie non-euclidee.Renato Pettoello - 2010 - Rivista di Storia Della Filosofia 65 (3):483-506.


Added to PP index

Total views
126 ( #92,586 of 2,505,211 )

Recent downloads (6 months)
31 ( #28,947 of 2,505,211 )

How can I increase my downloads?


My notes