Beltrami's model and the independence of the parallel postulate

History and Philosophy of Logic 9 (1):13-34 (1988)
E. Beltrami in 1868 did not intend to prove the consistency of non-euclidean plane geometry nor the independence of the euclidean parallel postulate. His approach would have been unsuccessful if so intended. J. Hoüel in 1870 described the relevance of Beltrami's work to the issue of the independence of the euclidean parallel postulate. Hoüel's method is different from the independence proofs using reinterpretation of terms deployed by Peano about 1890, chiefly in using a fixed interpretation for non-logical terms. Comparing the work of Beltrami and Hoüel with the treatment of non-euclidean geometry after the development of the axiomatic method in the 1890s indicates an important shift in mathematicians? attitudes towards mathematical theories
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1080/01445348808837122
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 22,046
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
M. Kline (1978). Mathematical Thought From Ancient to Modern Times. British Journal for the Philosophy of Science 29 (1):68-87.
J. Corcoran (1981). From Categoricity to Completeness. History and Philosophy of Logic 2:113.

Add more references

Citations of this work BETA

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

19 ( #206,457 of 1,934,441 )

Recent downloads (6 months)

2 ( #269,381 of 1,934,441 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.