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Thomas Reid's Discovery of a Non-Euclidean Geometry

Norman Daniels
Philosophy of Science
Vol. 39, No. 2 (Jun., 1972), pp. 219-234
Stable URL: http://www.jstor.org/stable/186723
Page Count: 16
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Thomas Reid's Discovery of a Non-Euclidean Geometry
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Abstract

Independently of any eighteenth century work on the geometry of parallels, Thomas Reid discovered the non-euclidean "geometry of visibles" in 1764. Reid's construction uses an idealized eye, incapable of making distance discriminations, to specify operationally a two dimensional visible space and a set of objects, the visibles. Reid offers sample theorems for his doubly elliptical geometry and proposes a natural model, the surface of the sphere. His construction draws on eighteenth century theory of vision for some of its technical features and is motivated by Reid's desire to defend realism against Berkeley's idealist treatment of visual space.

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