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Thomas Reid's Discovery of a Non-Euclidean Geometry

Published online by Cambridge University Press:  14 March 2022

Norman Daniels
Norman Daniels*
Affiliation:
Tufts University
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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.

Type
Research Article
Information
Philosophy of Science , Volume 39 , Issue 2 , June 1972 , pp. 219 - 234
Copyright
Copyright © 1972 by The Philosophy of Science Association

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References

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