A thought experiment: Kant vs non-Euclidean geometry

Question

Relevant question: What was the impact of the discovery of non-euclidean geometry on Kantian thought?

First question is that I wonder:

• Had Kant ever got his hands on some treatises about the early non-Euclidean geometry prototypes?

If the answer is yes, then Kant's claim on Euclidean geometry being synthetic a priori is certainly more of an issue to me (though I am a huge of fan of the A/B).

He certainly can have the following kind of thought experiment:

Imaging a creature that lives in a place that parallel lines can intersect with each other, does Euclidean geometry provide the a priori spacial-temporal framework that enables this creature to perceive the world?

For example, we view the sphere S^2 as R^2 union with the infinity (we can view infinity as the north pole), then two lines of two different fixed longitudes, are parallel to each other, yet indeed intersect with each other at the north pole.

Back to the thought experiment, we can definitely imagine this creature lives somewhere in this universe, maybe besides a place that the space-time is so curved, so that what an individual of this creature perceive are all non-Euclidean, light is bent, time flows differently when you step a little towards the gravity well, etc.

Or seeking the synthetic a priori for another creature is like seeking noumena?

I am not formally trained in philosophy, so this question may sound stupid. Thanks in advance.

Answer 1

Kant is interested in space as you see it when you open your eyes. When I look out of my window I do not see parallel lines meeting at infinity (perspectivally we do, but that is a completely different question). Kants isn't investigating either theoretical questions of geometry nor of space & time - he's more concerned about our immediate perception of space & time. He's specifically interested in where consciousness meets space and time (not the two together - that is spacetime - we don't immediately perceive the space time metric).

No doubt he would have been interested in the theoretical possibility of non-euclidean geometry and also of the curvature of physical space-time had they been discovered then - he had been scientifically inclined until he moved decisively towards philosophy. In fact it was Humes critique about the possibility of science that woke him up from his 'dogmatic slumber'.