system
Given the following post, respond as if you're commenting on Reddit:
human
Kant's Left Hand Thing

Hey, guys, I'm kind of an amateur student of philosophy, just getting myself started. I picked up a book that's an introduction to important philosophical ideas, and I found myself on one that I just don't understand.

The page called it "Kant's Left Hand" and it was about Kant's answer to an argument between Leibniz and Newton about space. Newton was arguing that space is laid out on a grid, and that if all of the particles in space were moved, space would be different. Leibniz, on the other hand, was saying that space's coordinates are only things as they relate to on another. So Kant came up with a thought experiment where he imagined a universe with only a left hand, and a universe with only a right hand, and drew the conclusion that Newton was right.

So... What's going on with this? I'm seriously confused about all of it, and especially in how Kant was able to solve it with an experiment that  I don't feel proved a single thing.
gpt
You're on the right track here, but your characterizations of Leibniz, Newton, and Kant are all a little off. 

The dispute between Newton and Leibniz had to do with whether space was something independent of the objects located and situated in space. Newton said yes, and the theory articulated in his *Principia* both required and defended this position. He thought that locations in space are absolute, and they are exactly where they are independently of where ever objects might happen to be in space. Google his famous "spinning bucket" thought experiment for more details on this. 

Leibniz held a relationalist theory of space, and he said that positions in space were mere relations between objects. There are no facts about space independently of there being spatial objects with spatial relation to each other. 

To get a sense of where their disagreement lies, imagine the following scenario: Every single object in the universe is suddenly moved 5 inches to the left. According to Newton, a real change has occurred, because now everything is in a different position. According to Leibniz, no change has occurred at all, because the relation between all objects remains exactly the same as it had been before. 

Here's where Kant comes in. His argument is really just against Leibniz, not pro Newton. The main thrust of Leibniz's argument for relationalism was that spatial relations can only be cashed out in *conceptual* terms. That is, one can describe all spatial relations in terms of concepts like, "is 5 feet from", "is above", etc. Kant showed that mere conceptual relations cannot capture all there is to spatial relations. The two gloves example demonstrates this. If you take a right-handed glove and a left-handed glove, all the relations between the various parts of the 2 gloves are the exact same. For instance, the tip of the thumb is 2 inches from the tip of the middle finger, whether you are considering the left or the right glove. And if you describe each and every relation between the various parts of any one glove to all the other parts of that glove, then the set of relations you come up with for the left-handed glove will be the exact same as what you come up with for the right-handed glove. But if Leibniz's theory were correct, this would mean that the right and left gloves were exactly identical. But that's obviously not correct. There is something undeniably different between a left and right glove. This means, at least according to the Kant of the 1780s (he used the thought experiment for different purposes in earlier parts of his career), that space is not merely a set of relations between objects, but must have a status above and beyond that. So suck it Leibniz.