Genz II 19
Kant/Geometry/Genz: Kant did not yet know that the angular sum of the triangle on a spherical surface is > 180°. (Only Gauss, a few decades later, thought it possible, but his experiment did not show it; the curvature is too small.).
Genz II 20
N.B.: non-Euclidean geometry becomes empirical science, not a priori.
>
a priori, >
Euclid/Kant.
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Thiel I 281
Space/Geometry/Thiel: the meaning change of the terms "space" and "geometry" is more confusing. Kant is always the guardian of the conservative Euclidists.
Space/Kant: plural of space only in the sense of parts of the same space.
Non-Euclidean Geometry/Kant/Thiel: little is known that Kant 20 years before the "Critique of Pure Reason" (From the true estimate of the living forces) considered other approaches possible:
That the physical bodies act differently to one another according to the Newtonian law of gravitation, that the space has a different dimension number than 3 ...
I 282
"... a science of these possible types of space would be the highest geometry ... such spaces cannot possibly be related to those of a very different nature, they would have to be other worlds."
The possibility of coexistence is denied, but the possibility of existence is acknowledged. That this no longer occurs in the "Critique of Pure Reason" lies in the fact that Kant now wants to find the conditions of the possibility of life-world and scientific experience, and, of course, the unity of real experience excludes the coexistence of different "possible types of space."
I 283
The question of "true" geometry in Hilbert's sense has no meaning at all, since the axioms are propositional schemata, and schemata cannot be true or false.
>
Axioms.
I 284
In the 20th century, there was an attempt to fill the geometry conception with new content. (Relatively banal: the proof of the uselessness of Euclidean geometry by the fact that in cosmic sizes, the angular sum is greater than 180° in the case of measured light rays which are used as straight lines).
