Kant’s paradox

Square Paradox

The paradox Kant raises in the Prolegomena to Any Future Metaphysics, §13, is that two intrinsically alike objects must be interchangeable. However, some objects are exactly intrinsically alike, but they’re not interchangeable. He noted that his right hand is virtually identical to its image in the mirror. However, he could not replace his right hand with its mirror-image. He then proceeded to state that he could not think of any “internal difference” (Prolegomena, p. 37) between his right hand and its image in the mirror. Yet he could sense the difference between them for they were not truly congruent.
The image in the mirror wasn’t oriented identically to his right hand, for it was left-handed. The ability to sense the difference between two identical appearances, incongruity, implies that the location of these two distinct appearances was sensible. Therefore, he argued that his right hand and its mirror image were not representations of things as they are in themselves, but instead, they were representations of appearances, of sensibility, or how the hand and its image appear to him. He defined these representations as “sensuous intuitions,” and concluded that space is the external form of  these “sensuous intuitions.”
Kant seems to be arguing that space is a property of objects as they appear to us, because for objects in themselves, if they were identical they would be congruent, or occupy the same space, and appear as a singular object. The crux of the argument lies with the premise that space cannot be a property of an object in itself, given the paradox of two identical images, or appearances that are not congruent. The right hand is identical to its mirror image, except that the image is a counterpart. I can see, or “sense,” that my right hand is the converse of its counterpart as a left hand, because I am aware of the concept left and right. Therefore I can distinguish the counterpart because I have the ability to immediately recognize identical objects in different locations. Kant concludes we are able to detect incongruity because space is a property of objects as they appear to us.
Kant’s argument is valid, but whether he can argue that space is intuitive depends on the nature of space in itself. Given that there are far more dimensions than what we can intuit, or perceive, (the number may even be infinite!) then Kant’s argument loses its universal and necessary status as a synthetic a priori. Perhaps Kant’s argument can be rescued as long space-for-beings and space-in-itself is distinguished.
Immanuel Kant, Prolegomena to any Future Metaphysics, tr. Gary Hatfield 1997 Cambridge University Press

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...a philosophisticator who utters heresies, thinks theothanatologically and draws like Kirby on steroids.

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