Comparing Kant's 'Transcendental Idealism About Space'

Prompt #4
Kant on Incongruent Counterparts
Consider the two spherical triangles △ACB and △ACB’ in Figure 1 on Page 6, which have all their three sides and three angles equal. It would thus seem that these two triangles are identical, or to use a mathematical term, congruent. However, Kant notices something quite paradoxical about them: people ordinarily think it’s necessary for two congruent objects to occupy the same space if they are put in the same place, but it’s impossible to demonstrate that △ACB and △ACB’ can occupy the same space, since △ACB can be moved only to △ACB’’ as illustrated in Figure 2 (Proleg 4:285–286). Kant calls objects such as these two triangles a pair of incongruent counterparts, from which he develops an argument

Kant argues that transcendental realism about space lacks the necessary explanatory power to account for the existence of incongruent counterparts, whereas Kant’s preferred view, namely transcendental idealism about space, can explain it (4:286). The latter view proposes that
Transcendental Idealism about Space: Spatial properties had by objects are somehow dependent on human sensibility.
The first section of this essay will be devoted to an explication of Kant’s argument. In the second section, I consider how the argument is significant for Kant’s larger project in the Transcendental Aesthetic. Finally, I offer a critical discussion of the argument.
I. The Argument
As suggested in my introduction, Kant’s argument can be understood as both an argument against transcendental realism about space and one for transcendental idealism about space, which I will refer to as the negative argument and the positive argument, respectively. I begin with the positive argument and Kant’s first argumentative step is to show that transcendental realism about space yields some sort of paradox (4:285).
Kant starts with a fairly uncontroversial test for

The next argumentative step Kant makes is to argue that this paradox is in explicable in transcendental realist terms: transcendental realism about space regards spatial properties as some intrinsic, “real” properties that objects have, but there is just no intrinsic difference between the incongruent counterparts that could possibly account for the different space which they occupy (ibid.). From this line of thought, we can finish constructing the negative argument against transcendental realism about space:
Q1. If transcendental realism abut space is true, then the incongruity of a pair of incongruent counterparts must be explicable in terms of some different intrinsic property.
Q2. △ACB and △ACB’ are a pair of incongruent counterparts, but their incongruity is inexplicable in terms of some different intrinsic property.
Q3. Therefore, by modus tollens, transcendental realism about space is