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In their book "Von Glückzahl bis Geheimzahl" Christian Hesse and Karsten Schwanke write:

As far as the absoluteness of space is concerned, Kant gave the so-called argument from the first piece of creation for this. He fictitiously assumes that the very first thing in an otherwise completely empty world is a single human hand created by God. This single human hand must inevitably have been either a right or a left hand. It was not possible to leave it completely undetermined in terms of the division left or right. For if that were the case, and if God subsequently created a handless body, it would have to fit on both sides of the body. "Which is obviously impossible", as Kant concluded.

Here, however, Kant committed a mistake in thinking which he himself later noticed and which caused him to depart from absolute space. By letting God create an actionless body, the situation is fundamentally changed and the problem eliminated. For then one can define the first created hand in relation to this body as a right or a left hand.

To be honest I cannot understand this line of thought. Could anybody explain the argument and to which part of Kant's work it is referring?

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  • Would you like to see a hand with no handedness?
    – Joshua
    Aug 11 at 1:30
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This is variously called the "argument from incongruent counterparts" (Harper, Kant on Incongruent Counterparts) or the "argument of the solitary hand" (van Cleve, Right, Left, and the Fourth Dimension). It appears in one of Kant's last pre-critical works Concerning the Ultimate Ground of the Differentiation of Directions in Space (1768), where he defended Newton's absolute space against Leibniz's relational one (which he supported previously). It was a way station on his path to the reinterpretation of space and time as neither absolute nor relational entities, but rather forms of our intuition. Here is van Cleve's exposition of the argument and objections to it:

"Externalism maintains that a hand's being left or right depends on how it is related to other material objects-in particular, on how it is related to other asymmetrical objects like human bodies. This is the position Kant sought to refute by the famous thought-experiment of the solitary hand. Imagine a hand all alone in the universe; would it not be either left or right? If so, handedness cannot depend on relations to other material objects, for ex hypothesi there are none.

Some of Kant's critics, notably Peter Remnant and Martin Gardner, have responded to this thought-experiment by simply denying that a solitary hand could be left or right. According to them, a solitary hand would simply be indeterminate or neuter... Gardner takes Kant to be arguing as follows: Consider a universe whose only material object is a human hand. If a handless human body were introduced alongside the original hand, the hand would have to fit either the right or the left wrist of the body, and would therefore be either right or left. But the introduction of the body would not change the hand in any way; therefore, it must have been right or left all along.

If this were indeed Kant's reasoning, it would be open to the following parody: Consider a universe that contains nothing but a single ball. If another object, larger or smaller than the ball, were introduced into the universe, the ball would (in relation to it) be either large or small. But the introduction of the second object would not change the ball in any way. Therefore, the ball must have been large or small all along. Here the conclusion is absurd and the fallacy leading to it not hard to spot. Nothing is large or small simpliciter, but only in relation to something else..."

He further explains that both Kant's reasoning and Gardner's objection are more subtle than that (for one, handedness is not relative in the same sense as size), but a common view has been that Kant's argument is, in the end, unsuccessful. Rukgaber recently proposed a defense of it though in The Asymmetry of Space: Kant’s Theory of Absolute Space in 1768:

"Commentators have continually argued that Kant’s argument is an utter failure that shifts from the metaphysics of space to its epistemology, because he has no way to connect ‘directionality’ and ‘handedness’ to absolute space. This supposed failure is based on an understanding of absolute space in purely mathematical terms and as an absolute void that lacks any qualitative or dynamic features. If we recognize that Kant held that space had an intrinsic directional asymmetry then his argument successfully connects incongruent counterparts to absolute space."

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  • And it turns out that space has an intrinsic rotational asymmetry written into the laws of physics after all.
    – Joshua
    Aug 11 at 1:28
  • @Joshua Which rotational asymmetry are you referring to?
    – Galen
    Aug 11 at 4:33
  • @Galen: Presumably the weak nuclear force, although I'm frankly not sure I would call that an asymmetry of "space" per se.
    – Kevin
    Aug 11 at 5:25
  • According to Rukgaber, "Kant thought of space as a dynamic force, emanating from ‘attraction points’, which was once a varied field of intensities that then gave rise to all observable matter in motion and left behind a rarefied material space, which appears as our present, seemingly empty space... The primary matter or elementary Urstoff of the universe has a single directional rotation". If he is right, Kant's "absolute space" was very far from Newton's and had physical, in addition to geometric, properties. It was more like aether than space.
    – Conifold
    Aug 11 at 5:46
  • @Kevin: Depends on your point of view. The chirility of the weak nuclear force and the predominance of matter over antimatter are coupled to the direction of time.
    – Joshua
    Aug 11 at 14:13
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I will clarify one part, completely and solely from a spatial coordinate standpoint

From that perspective, here is what Kant did not immediately know:

Handedness, or “chirality”, is a fundamental property not definable linearly. Knowing what right and left means is equivalent to knowing how orientation (clockwise or counterclockwise) is defined. It is not arbitrary but a fundamental property of geometries that are not symmetric about their axis. It is built into physics problems based on our definition of the positive directions of three dimensional coordinates (or similarly the positive direction of angles in polar coordinates), or by the direction for the positive of the cross product of two vectors, and often employed with “the right hand rule”.

We must refer to something with chirality to define right and left. Length, time, mass (including its sign), and charge (including its sign) also cannot be communicated without referring to something.

Kant assumed handedness was arbitrary. You can see long discussions by physicists about how you would communicate right and left to an alien civilization. It is hard. It takes something spinning that you can both see, and a direction to define from which side you’re looking at the spinning thing (a spinning galaxy you can both see for example). Having that, you can say, “Seen from that side it is spinning a direction we define as ‘clockwise’, and the top of the circle is going in a handedness direction we now define as ‘right’.” A more recent solution is that a neutrino has only one direction of spin due ti its parity violation, and it can be used to define right and left. Yes the chiral symmetric human body makes this important, but it is important for much more.

Summary

If a neutrino has handedness, if the milky way seen in the direction of cosmic radiation has handedness, then a floating hand has handedness. It has chiral asymmetry that is not arbitrary and not relative to any orientation, direction, or other object.

However, our name for chirality “handedness” and the use of the human hand as the quintessence of a chiral form both certainly do come from our more relative aspects.

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