…t isn’t so surprising that geometry can give us eternal truths without the need for empirical data. Since space is a formal condition of all our experience, understanding the necessary properties of space itself gives us geometric solutions that must generalize for everything presented to our experience.
This is a salient truth of pure mathematics, which largely is about formalization of mathematical spaces.
Only after a space has been parameterized can elements of the space be studied. What can be experienced in the space then is bounded by the parameters of the space. Given there exist axioms that govern parameterization of spaces, robustness of such parameterization always can be ascertained.
Consider then that if people believe in impossibility of metaphysical truth, all scholars within that field will do is come up with their own basic theories of that truth, with outcome a progressive literature never develops. Would it not be better to start off with some foundation that can split in many different directions that then can be built upon in again many different directions?
In this way, uniqueness of thought can be maintained, yet in relation to some central core concepts with which there either is congruence or non-congruence.
As either of congruence or non-congruence grows the core evolves, and can be reformulated as necessary.
It never is possible to build anything new and meaningful if there is a wait for certainty prior to commencement of the project.