Les triangles sphériques et le paradoxe des objets non congruents
Kant has been concerned with the problem of incongruent counterparts at different moments in his career: for instance in his 1768 article on the directions in space, in his Dissertation of 1770 and in the Prolegomena (1783). The purpose of this article is to demonstrate that 1) the example of the spherical ‘scalene’ triangles is the only one (thus excluding the isosceles and equilateral triangles) that can support Kant’s argument about the intrinsic character of the difference between two similar but nevertheless incongruent spherical triangles, 2) that what is here philosophically at stake is Wolff’s erroneous conception of “similarity” in geometry, and 3) that Kant’s thesis on the intrinsic nature of the difference between incongruent counterparts in space remains valid for his conception of space as “absolute” in 1768 as well as for his view of space as an a priori formal condition of the possibility of experience in 1783.
Kant, Wolff Incongruent counterparts Geometry Spherical triangles