Ok so now I am FINALLY starting to get the space arguments. After rereading them in light of the kind elucidation given by my fellows here it finally became a little clearer. Kants reasoning is actually VERY straightforward in these arguments and almost childlike in its simplicity.
Now the one that still eludes me is the incongruent counterparts argument.
I want to get a good mark so Im adding this badboy into the mix for extra points but so far I havent been able to fathom it.
My question is, what is it saying and how does it relate back to the other 4 argument given in the critique?
‘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.’
My tutor gave me this to explain it: Incongruent Counterparts: the aim here is to give a reason why space is not a concept but an intuition. Basic claim is that the right hand and the left hand are counterparts i.e. that they have all the same basic characteristics. What makes them incongruent with each other however is the fact that one hand is right and the other is left. Kant is asking us to think what this difference consists in since the incongruence is marked in the fact the right hand has something about it that the left does not and vice versa. The difference is
not conceptual: this is what he is trying to show.
I think I may have an idea what is going on here…
So, with the right and left hand argument, we could not tell if it was either through conceptual means precisely because there is only one, similarly to our knowing that a two lines of a triangle are greater than the third side only through a priori intuitive means. So, we tell that the glove/hand is either right or left not empirically but a priori. But wouldnt the knowledge of left and right hands have come originally from an empirical source?
Tell me if Im on the right track and ammend as is necessary! 