An Addition to "Immanuel Kant and Non-Orientability"

It is interesting that Kant's fondness for issues of handedness has come up in two courses of mine so far this year. I first ran into it in PL21 (Science, Perception, and Reality, Prof. Nick Huggett). Here we ran into Kant when discussing space. The question at hand is, is space actually a physically existent "something" (as Kant and others, collectively known as substantivalists) believed, or is it merely a convenient way of referring to the relationships of distance we perceive in objects. Those who adhere to the latter precept (that space is relative) are known as relationists.

The argument between substantivalism and relationism is long one, with many stock arguments and responses. Kant, for his part, added to this repertoire using handedness as an argument for substantivalism. Kant asks us to imagine, for instance, the two hands of some ideally symmetrical individual. The relationist, by the nature of his position, is required to explain all physical phenomena in terms of relations between objects. Kant points out that the relationist is hard pressed to explain just what the difference is between a right hand and a left hand. After all, the tip of either thumb is exactly as distant to the tip of the corresponding forefinger as are the corresponding points on the other hand. Kant then argues that this is evidence for a real, existent space, since this property of "handedness" is one that cannot be explained in terms of relational distances.

The relationist response is fairly compelling to me. The important thing to realise is that simply using terms like "right-handed" and "left-handed" implies a relation. Kant wants us to think of handedness as some sort of immutable property of objects, whereas it is really merely a human convention; when we say that a hand is left-handed, we mean that it fits into left gloves. This idea of handedness as a result of fitting is sufficient to defuse Kant's attack.

I hadn't realized that Kant had used a similar argument (and equally fallaciously, to my way of thinking) against higher dimensional geometries. I found that rather interesting.