Beltrami's model and the independence of the parallel postulate

History and Philosophy of Logic 9 (1):13-34 (1988)
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Abstract

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

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References found in this work

Mathematical Thought from Ancient to Modern Times.M. Kline - 1978 - British Journal for the Philosophy of Science 29 (1):68-87.
Philosophy of Geometry from Riemann to Poincaré.Nicholas Griffin - 1981 - Philosophical Quarterly 31 (125):374.
From categoricity to completeness.J. Corcoran - 1981 - History and Philosophy of Logic 2:113.
What is Mathematics? [REVIEW]E. N. - 1942 - Journal of Philosophy 39 (8):221-221.

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