History and Philosophy of Logic 28 (1):19-30 (2007)

David J. Stump
University of San Francisco
I trace the development of arguments for the consistency of non-Euclidean geometries and for the independence of the parallel postulate, showing how the arguments become more rigorous as a formal conception of geometry is introduced. I analyze the kinds of arguments offered by Jules Hoüel in 1860-1870 for the unprovability of the parallel postulate and for the existence of non-Euclidean geometries, especially his reaction to the publication of Beltrami’s seminal papers, showing that Beltrami was much more concerned with the existence of non-Euclidean objects than he was with the formal consistency of non-Euclidean geometries. The final step towards rigorous consistency proofs is taken in the 1880s by Henri Poincaré. It is the formal conception of geometry, stripping the geometric primitive terms of their usual meanings, that allows the introduction of a modern fully rigorous consistency proof.
Keywords Beltrami  geometry  consistency
Categories (categorize this paper)
DOI 10.1080/01445340600758800
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 70,130
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

Philosophical and Mathematical Correspondence. [REVIEW]A. Reix - 1982 - Revue Philosophique de la France Et de l'Etranger 172 (1):64-64.
The Foundations of Geometry.David Hilbert - 1899 - Open Court Company (This Edition Published 1921).
La Science et l'Hypothèse.H. Poincaré - 1903 - Revue Philosophique de la France Et de l'Etranger 55:667-671.

View all 19 references / Add more references

Citations of this work BETA

Add more citations

Similar books and articles


Added to PP index

Total views
33 ( #345,631 of 2,506,405 )

Recent downloads (6 months)
1 ( #416,997 of 2,506,405 )

How can I increase my downloads?


My notes