incongruent counterparts

(or incongruous counterparts )

Spatial items which relate to each other as mirror-images do, so that although the same shape, they cannot be superimposed so as to occupy exactly the same volume of space. In three dimensions, a right hand cannot occupy exactly the same space as a left hand. On a two-dimensional plane, a letter L cannot be moved to cover the same letter L reversed. It is notable that in three-dimensional space the letter can be flipped over to cover the reversed version. Similarly, if there were a fourth dimension of space, we could in principle disappear from the three familiar dimensions, flip round, and return with, for instance, our hearts on the right hand side of our bodies. Kant (Metaphysical Foundations of Natural Science, i. 13) advances incongruent counterparts as a problem for a purely relational theory of space. If we imagine a universe with just one object, say a single hand, it would seem to be determinate whether it is a left hand or a right hand, yet all the spatial relations of its elements will be the same whichever one it is. So a relational theory of space seems unable to account for the difference, and therefore seems to be inadequate.