Cambridge 1715: A Meeting At Trinity College [1]

Georg Bengtsson, 2021

Eleni Ieremia, ”An invitation”, 2019

Newton: Thank you for coming, Gottfried. I have greatly looked forward to our meeting. I understand that you wanted to discuss some of the things I’ve written about your relational approach on the subject of space.

Leibniz: Indeed. My view is that you’ve failed to refute the concept of relative space, and that your own theory is lacking, but of course, you knew this already. However, before we get ahead of ourselves, perhaps it would be best to start at the beginning. You’ll present your view, then I’ll present mine, and then we can take it from there.

Newton: The beginning does sound like a natural place to start. Very well, then, would you like me to explain the basic concepts first and then move on to the theory behind it, or should I start in the opposite direction?

Leibniz: I think it best if you would go through the basic concepts first, so that there’s no chance of misunderstandings later.

Newton: Of course. I will begin by explaining how Absolute Space is supposed to be understood, I’ll then go through my arguments for its existence, and we’ll see what you have to say.

Leibniz: Go ahead.

Newton: My reflections on this topic began with my ambition to construct a science of motion. I found that for a science of motion to be possible, one needs a concept which explains what exactly it is that bodies move through. I therefore changed the course of my studies to the topic of space, its nature, and its form. For when we think about space, it is natural for us to assume that space is not something that exists in any absolute sense. You can’t touch it, you can’t exactly see it. You can merely infer it by noticing that different objects are in different places – and it seems as if it can’t be described as having a form.

Leibniz: So far, you haven’t said anything contentious on the nature of space, except perhaps that you can infer it by noticing the different positions of bodies.

Newton: Of course not. But neither am I finished. As my studies progressed, I found it more and more obscure to talk of space as something non-existent.

Leibniz: And why is that?

Newton: Well, take, for example, a sailor who moves around in the bowels of his ship. The sailor is himself in movement relative to the ship, but the ship itself is also in movement relative to the ocean. We might think of the ship as a type of container that is in itself movable. But if we wish to claim that the ship is movable, we must identify another, larger container, for the ship to move through. We must continue with this process until we either have an infinite number of movable containers, or simply one, infinitely large container that cannot be moved. This immovable container I call Absolute Space, and it is absolutely necessary to accept the existence of it, if we wish to say that objects can move, in any true sense. For at one point, the sailor is in a certain place inside of the ship, and the ship is in a certain place on top of the ocean. At a later point, the sailor will be in a different place on the ship, and the ship will be in a different place on the ocean. If we wish to say that objects actually go to different places when they move, it is necessary to accept the existence of Absolute Space. Otherwise, it would be nonsensical to speak of the movement of bodies.

Leibniz: I see plenty of problems with viewing space as something absolute. It seems to me as if your theory of space brings with it a number of odd consequences. For example, imagine a universe identical to our own, but where all the heavenly bodies are situated ten meters to the left of where they are in our own universe. Would we be able to tell the difference? What if they were situated ten million meters to the left? Would we then be able to tell the difference? Surely, we wouldn’t be able to. For as long as all the bodies have the same distance-relations to each other in this hypothetical universe as they do in our own, this second universe would be indiscernible from ours – they would be identical. But if we are forced to accept the existence of Absolute Space, then it would follow that these universes are different from each other.

Newton: I don’t see the issue.

Leibniz: The issue, my dear sir Isaac, is that it would contradict the principle of the identity of indiscernibles, which says that two objects – in this case, our two universes – are identical if they are indiscernible. If two objects have all their properties in common, they cannot be different.

Newton: I would simply claim that they do not have all their properties in common, since they have their bodies situated in different parts of Absolute Space.

Leibniz: Now you are presupposing that which has to be proven.

Newton: Fine. I see your point. The crux of your rebuttal, however, lies in the phenomenon of movement. You have failed to present an adequate theory of movement that excludes the existence of Absolute Space.

Leibniz: Then I will present my own view, which I believe you will find satisfactorily includes the phenomenon of movement.

Newton: Please do.

Leibniz: My own view, as you know, is that space only exists in a relative sense. Space is quite simply the distance between bodies. When we want to describe where objects are we must compare the object we wish to discuss with another object. I’ll explain what I mean using your own example. Let’s imagine a universe consisting of only one single ship. It wouldn’t make any sense for us to ponder where the ship is located or – to use your terms – what place the ship is in. If there are no other bodies to compare the placement of the ship, it would be obscure to claim that the ship is at a certain place. Only if we add another object, the sailor for example, can we make claims about where the ship is – but only in relation to the second existing object, namely the sailor.

Newton: Before you go on, I’d like to point out something that seems problematic to me.

Leibniz: I doubt it will be anything of importance but go ahead.

Newton: How do you explain extension? Objects take up space. My point is that even if it would be odd to ask where this lone ship is situated in this barren universe of yours, we must surely agree that the ship has an extension. What is it extended through, dear Leibniz, if not space?

Leibniz: If you would simply look closer at the concept of extension, you would see that it doesn’t pose a problem for my theory. Objects are indeed extended, but extension is not a substance existing in itself, neither is it an attribute of space. An extension of something is indeed just that, an extension of some thing. The fact that our ship is extended simply means that the ship has the attribute of extension. It does not need to be extended through something for it to contain this attribute, since the attribute is simply a part of the object itself.

Newton: I must admit that I find your answer doubtful, but let us not linger too long on this topic. Do go on.

Leibniz: So I shall. When we want to speak about movement what we are actually describing is a change in the distance-relation between two objects. When an object moves, it does so in relation to another object which is at rest. This means that whenever we want to describe an object as moving, we do so in relation to ourselves, or to another object at rest. Let me illustrate with an example. When we sit in a carriage going down the road, the carriage will be in movement in relation to the trees and houses it passes, but alas, from the view of the carriage it looks like the trees and the houses are the objects in motion. This means that we can never know for certain which objects are in movement and which ones are at rest. However, there is indeed movemnt, since the distancerelation changes over time, so while we can never be certain which object is moving, and which object is at rest, we can be certain that there is movement.

Eleni Ieremia, ”An invitation”, 2019

Newton: I am sorry to say that I find this view unsatisfactory for two reasons. The first being that if one were to claim that the sun revolves around the earth while another claims that the earth revolves around the sun, they would simply be saying the same thing using different words – but surely, the two claims are contradictory? The sun cannot, in any true sense, revolve around the earth, at the same time as the earth revolves around the sun. What your theory implies is that these two statements mean the same thing, which seems to make things awkward for the church and Galileo. My second reason for disliking your theory is that you don’t only need space to be relative, but motion seems to be made relative as well. Things do not truly move in your view of the universe; this I find greatly unsatisfactory.

Leibniz: First of all, those two sentences do not mean the same thing. They are merely said from two different perspectives: One from the perspective of the sun, the other from the perspective of the earth. Secondly, things do truly move according to my view of the universe; we are simply unable to determine true motion. Since it is impossible to see which objects are truly at rest, it is equally impossible to determine which objects are in motion. It seems to me that your view is grounded on nothing more than a wish. I agree that it would be practical if Absolute Space were to exist, but so far there doesn’t seem to be anything that might be deemed as proof of its existence.

Newton: I have proof.

Leibniz: You have proof?

Newton: I have proof of the effects of Absolute Space.

Leibniz: I suppose you’d like to present it then.

Newton: Yes. I would like us to yet again – but for the last time – imagine a completely barren universe. In this great ocean of nothing, we shall add a bucket, and fill it with water. Next, we will give the bucket a push, so that it starts to rotate. The water in the bucket will at first be still and then it will start to concave along its surface as it starts to rotate due to the friction from the bucket. This means that the water has a tendency to recede from the center of rotation. Now if all movement were relative, we would have to explain the phenomenon of the water receding from the center of rotation by relating it to the walls of the bucket. But this cannot be done. Therefore, the water in the bucket has to be in absolute motion, meaning that it has to move through Absolute Space as it rotates. Since it is impossible to explain this phenomenon using relative motion and relative space, we must conclude that Absolute Space exists. If you are doubtful of this answer, we could go out into the garden and I’ll give you a demonstration.

Leibniz: That won’t be necessary, my dear Newton. I see now that we differ in ways that debate can never change. In your mind, your bucket proves the existence of Absolute Space, but only if we agree to your science of motion, and I do not. I believe you to be the greatest jewel learned England has ever had, but on this occasion you must be wrong. Our good God created our world and put everything in its perfect place. But it would be an arbitrary choice to put the sun, the earth and the moon where they are now, instead of somewhere else, if Absolute Space were to exist. It would contradict His infinite wisdom to make a choice so trivial when all His other choices are made for reasons so divine mortal men like us could never fully understand them. Therefore, your theory of Absolute Space can not be true. It must not be true. And with this I say good day.

[1] In the following dialogue, the author makes use of the fictional characters Isaac Newton and 1 Gottfried Willhelm Leibniz to represent the real Newton’s and Leibniz’ different perspectives on space. Newton and Leibniz never met, and the correspondence that this dialogue is mostly built upon is in fact a correspondence between Leibniz and Samuel Clarke, an English philosopher who believed that Newton had managed to prove the existence of Absolute Space in the Scholium.