Some boys and girls find it very difficult to learn which is their right and which their left hand. Likewise, when they begin writing, some confuse their p's and q's, or their b's and d's. Kant had the brilliant insight that children are right to be confused. Something deeply puzzling is involved. In a famous argument published in a four-page essay in 1768, Kant diagnosed the children's problem and found in it a beautiful justification for Newton's absolute space.

Kant's startling argument

If two objects have the same size and shape, they are called “congruent”. If an object is removed from a place exactly its size, a congruent object can be put in the same place. But your hands are “incongruent”: they have different shapes. A left hand cannot be inserted into an empty righthand glove. This gave Kant pause. Hands have similar parts and yet are incongruent. He called two incongruent objects that have the same parts arranged in the same way, incongruent counterparts. They are a pair of counterparts because they are so similar, and yet they are incongruent.

What makes left and right hands different? They each have the same number of fingers, and each of the fingers is attached to a palm. What accounts for their difference? We want to say that the fingers point “in different directions”, but surely a direction outside the hand cannot determine the hand's shape.