David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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)|
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
Nicholas Griffin & Roberto Torretti (1981). Philosophy of Geometry From Riemann to Poincare. Philosophical Quarterly 31 (125):374.
Citations of this work BETA
No citations found.
Similar books and articles
Alf Onshuus (2006). Properties and Consequences of Thorn-Independence. Journal of Symbolic Logic 71 (1):1 - 21.
Jamie Tappenden (2000). Frege on Axioms, Indirect Proof, and Independence Arguments in Geometry: Did Frege Reject Independence Arguments? Notre Dame Journal of Formal Logic 41 (3):271-315.
Giovanni B. Grandi (2005). Thomas Reid's Geometry of Visibles and the Parallel Postulate. Studies in History and Philosophy of Science Part A 36 (1):79-103.
Rafał Gruszczyński & Andrzej Pietruszczak (2008). Full Development of Tarski's Geometry of Solids. Bulletin of Symbolic Logic 14 (4):481-540.
Michael Scanlan (1991). Who Were the American Postulate Theorists? Journal of Symbolic Logic 56 (3):981-1002.
David Stump (1991). Poincaré's Thesis of the Translatability of Euclidean and Non-Euclidean Geometries. Noûs 25 (5):639-657.
Michael Scanlan (2003). American Postulate Theorists and Alfred Tarski. History and Philosophy of Logic 24 (4):307-325.
Ricardo J. Gómez (1986). Beltrami's Kantian View of Non-Euclidean Geometry. Kant-Studien 77 (1-4):102-107.
David J. Stump (2007). The Independence of the Parallel Postulate and Development of Rigorous Consistency Proofs. History and Philosophy of Logic 28 (1):19-30.
Added to index2010-08-10
Total downloads14 ( #115,725 of 1,102,742 )
Recent downloads (6 months)1 ( #296,833 of 1,102,742 )
How can I increase my downloads?