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Full Idea
Russell sought what was common to Euclidean and non-Euclidean systems, found it in the axioms of projective geometry, and took a Kantian view of them.
Clarification
A 'Kantian' view relies on intuition
Gist of Idea
Geometry is united by the intuitive axioms of projective geometry
Source
report of Bertrand Russell (Foundations of Geometry [1897]) by Alan Musgrave - Logicism Revisited §4
Book Ref
-: 'British Soc for the Philosophy of Science' [-], p.109
A Reaction
Russell's work just preceded Hilbert's famous book. Tarski later produced some logical axioms for geometry.
10052 | Geometry is united by the intuitive axioms of projective geometry [Russell, by Musgrave] |
10053 | Geometrical axioms imply the propositions, but the former may not be true [Russell] |