Poincaré's thesis of the translatability of euclidean and non-euclidean geometries

Noûs 25 (5):639-657 (1991)
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Poincaré's claim that Euclidean and non-Euclidean geometries are translatable has generally been thought to be based on his introduction of a model to prove the consistency of Lobachevskian geometry and to be equivalent to a claim that Euclidean and non-Euclidean geometries are logically isomorphic axiomatic systems. In contrast to the standard view, I argue that Poincaré's translation thesis has a mathematical, rather than a meta-mathematical basis. The mathematical basis of Poincaré's translation thesis is that the underlying manifolds of Euclidean and Lobachevskian geometries are homeomorphic. Assuming as Poincaré does that metric relations are not factual, it follows that we can rewrite a physical theory using Euclidean geometry as one using Lobachevskian geometry and express the same facts.



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Conventionalism, structuralism and neo-Kantianism in Poincaré’s philosophy of science.Milena Ivanova - 2015 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 52 (Part B):114-122.
Poincaré on the Foundations of Arithmetic and Geometry. Part 1: Against “Dependence-Hierarchy” Interpretations.Katherine Dunlop - 2016 - Hopos: The Journal of the International Society for the History of Philosophy of Science 6 (2):274-308.
Carnap's metrical conventionalism versus differential topology.Thomas Mormann - 2004 - Proc. 2004 Biennial Meeting of the PSA, vol. I, Contributed Papers 72 (5):814 - 825.

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