Geometry, Intuition, Angle

As has been previously discussed, the lack of any Empirical evidence of geometrical figures in the non-Human world supports the Empiricist thesis that Geometry is the product of abstraction from the cognition of that world.  One standard response to the Empiricist is that the elements of Geometry compose the noumenal substratum of that world, accessible via a type of Intuition.  However, challenging for that response is to explain how perhaps the most fundamental of the elements, the Line, is at all even intuited without some phenomenal content.  So, less challenging in that regard is for another element--the Angle--an in-between that has no phenomenal content.  Of course, the Empiricist can argue that an Angle is nothing but an abstraction from two Lines, but the Intuitionist can respond that the Empiricist reduction fails to account for how the two Lines are arranged.  Still, another shortcoming of the thesis that the Angle is a noumenal existent is that as existing where there are two Lines, it is restricted to two-dimensionality, and, hence, is inadequate as a substratum of the three-dimensions of the empirical world.