Can you ever see an empty space?
By Joseph Edward Lucas 

The question of whether or not you can see an empty space is concerned with the nature of space and how our understanding of it is formed. Newton, Leibniz and Kant held contrasting views on this. I shall focus on the disputes between these three and attempt to draw my own conclusions from their work.

Sir Isaac Newton believed in an absolute and real space in Euclidean geometry. For him, space is a self-subsistent reality, ‘distinct from body’, a container in which all objects are placed. He spoke of Absolute Space in order to distinguish it from Relative Space, the way in which we measure Absolute Space whereas Absolute Space describes space itself. For Newton the immobility of space is a key aspect of its absolute nature. Newton argues as follows that Absolute Space is immobile:

As how the order of the parts of time are immutable, similarly is the order of the parts of space. Suppose then that that if those parts were moved out of their places, then they will be moved out of themselves, for space is the place of the parts themselves as well as other parts (in other places). Just as parts in time are placed in order of succession, parts in space are placed as to order of situation. It is therefore of their nature that parts are also places in space, the idea that the primary places of things should be movable is absurd. To continue the analogy, like as moving a part of time (seconds, minutes, hours etc.) from its primary place is ridiculous because for example you cannot simply move one hour of one day to a different day. Therefore Absolute Space is immobile.*1

You would thus never be able to see an empty space, as space itself is a collection of parts (objects), which themselves also make up space. As we know that objects exist, whether we can see them or not, a proton is an example of an object we can’t see, we must therefore always conclude that space exists. There is something rather than nothing, therefore space exists and as space is a collection of objects, it is impossible to see an empty space. According to Newton seeing an empty space would mean space itself not existing, something that by definition can’t ever be seen.

Leibniz very publicly rejected Newton’s ideas. He rejected “…the fancy of those who take space to be a substance, or at least an absolute being,” and added ironically that “…real and absolute space is an idol of some modern Englishmen.”2 Leibniz’s view on space was that it is not so much a thing in which bodies are located as systems of relations holding between them. He told Clarke in his third paper that he considered space to be “something merely relative” and considered it to be “an order of things that exist at the same time.”3 In contrast to Newton, Leibniz viewed space as something which is ideal or imaginary.

There are two main pillars to Leibniz’s argument. First he says that space and time are not containers, but an abstract structure of relations in which bodies may interact. To illustrate this point, in his fifth paper, he uses the analogy of a family tree. Unlike the relationship between an oak tree and its leaves, a family tree is not a thing that exists independently of its members (Fathers, Sisters, Cousins etc.), but is an abstract system holding together the relations within a family. The branch connecting a Mother and a Daughter for example is not a physical branch.

Second he says that space and time are an abstraction from relations between objects and that while these relations are not fixed, the relation between space and time themselves is fixed. He also says that space and time are at least two steps removed from his monads, his constituents of ultimate reality. The justification for this being that the relations between objects are a ‘well founded representation of ultimate reality,’ there is enough empirical evidence to suggest these relations exist and that space and time themselves are a representation of relations between objects. They are therefore a representation of the the representation of ultimate reality, of which his monads are the constituents.

According to Leibniz’s view of space and time, empty space would exist in the real world were it the case that two objects existed at a spatial distance with nothing between them. This, in fact, was something that Leibniz himself maintained. However morally speaking he was very much opposed to the idea of an empty space. His argument for this is that the actual world (existence) is the best of all possible worlds, as God is omniscient, omnibenevolent and omnipotent and as Leibniz took the medieval view that existence is better than non-existence, he concluded that the actual world must be a plenum (must be full). There- fore he concludes that it is actually immoral for an empty space to exist.

Kant’s views on space are a direct response to the views of Newton and Leibniz. This is very clearly shown in his Critique Of Pure Reason when he asks the question, ‘What, then, are space and time? Are they things which actually exist? Are they only determinations or relations of things, but such as would belong to these things even if they were not intuited?’ (CPR:A 22,23 |B 37,38) Kant refers to the Newtonian concept as the “real existences” view and to Leibniz’s concept as the view according to which space is “only determinations or relations of things.”

Kant consistently rejected Leibniz’s view that space was founded on the order of relations of things. To Kant this seemed to imply that the truths of mathematics, 3-dimensional Euclidian geometry in this case, were dependant on the existence of a world of things and events. This is absurd as mathematical objects (such as numbers for example) are different from and exist independently of physical objects. For example you can count to two in- dependently of counting two apples.

Kant’s other criticism of Leibniz’s view was that it does not allow us to distinguish between incongruent counterparts. He uses his fascination with the difference between a left handed and a right handed glove to illustrate this point in his 1768 essay On the Basis of the Difference of Regions in Space. Kant’s view on describing the difference between a left handed glove and a right handed glove, according to Jonathan Bennett, was that the distinction between the two cannot be captured using language, as if you describe each glove individually you end up with an identical description for both gloves. He said there- fore that a right and a left handed glove are incongruent counterparts, as if one glove were to be placed on top of the other they would not match identically. In Leibniz’s view of space, the description of the relation of the parts to the whole is the same with both

gloves. For example the relation between the thumb and the little finger. Kant then went on to say that if God had created just a single glove it would have to be either left handed or right handed and only by human observation would you be able to tell which it is. Newton’s view of space did not solve this problem for Kant either. He said, suppose space is a huge container with a single glove, there is still no way of distinguishing whether it is right handed or left handed without human observation.

This led Kant to decide that space is related to orientation and direction. He believed that the concepts of right and left handedness emerge out of subjective experience of being intersected by 3 planes, all at 90 degrees to one another. He says in the Prolegomena, “The difference between similar and equal things which are not congruent cannot be made intelligible by any concept but only by relation to their right and left hands, which immediately refers to intuition.” Kant views space therefore as neither a substance nor a phenomenon, but as a form of “sensible intuition,” as he puts it in the Critique of Pure Reason, that is, part of the structure of our concepts which allows us to represent the world.

In the first two arguments in the Metaphysical Exposition, Kant talks about the source of our understanding of space. In the first of these arguments he argues against empiricist accounts of space such as those held by Locke and Hume. He states in this first argument, ‘Space is not an empirical concept which has been derived from outer experiences.’ (B39 / A24,25) In order to represent objects as in a different part of space and to represent them as outside or alongside one another, the representation of space must be at the basis. In other words, one must already be able to represent an object being away from them or two objects being away from each other without having seen it. Physically seeing an object being in a different place depends on your prior representation of this.

In the second argument Kant states that, ‘Space is a necessary a priori representation which underlies all outer intuitions.’ (B 39 / A 24,25) This is because it is impossible to rep- resent there being no space at all. He says that space is to be regarded as ‘the condition of the possibility of all appearances, not as dependent upon them.’ Space allows us to view objects and its existence is independent of objects existing.

From the elements of Kant’s views on space and time I have discussed, we can say that within the Kantian view of space it would be possible to conceive of an empty space, as space is something we have knowledge of a priori, independent of objects. Kant says, ‘one can think of space without objects to fill it.’ We would not be able to see it however, as an empty space would not enable us to exist and we could therefore not physically see an empty space.

There is, however, a problem with Kant’s view that space and time are not objects but forms of intuition. He frames this view with the idea of the subject being intersected by three planes all at 90 degrees to one another. However, surely these planes are themselves mathematical objects. Kant could not have anticipated the Fregean view that mathematical objects are the referents of singular terms in true mathematical propositions. However it is possible to regard the three intersecting planes as objects in this sense. Therefore Kantian sensible intuition of space turns out to depend on the existence of objects, or at least the objectivity of mathematical truths, after all. The first problem with this is that Kant’s view is circular in presupposing that which it seeks to explain. Second, however, if the form of intuition of space depends on objects, then we cannot intuit an empty space, since the very concept of space is dependent on the existence of a certain kind of object.

Each of these views on space provides a very different insight into how to answer this question. According to Newton’s and Kant’s views it is not possible to ever physically see an empty space. Kant, however said that it would be possible to conceive of an empty space. According to Leibniz’s view it would be physically possible, but according to his views on emptiness it would be immoral for an empty space to exist. What these views lead to is a common conclusion that we would never be able to physically see an empty space in the literal sense. This, then however raises the semantic and epistemological question of what seeing is. Both Kant and Leibniz leave room for empty space as a conceptual possibility. However, this is fraught with difficulties for them. If it is possible to an empty space to exist it is hard to know what it would look like.

* Quoted in Stanford Encyclopaedia of Philosophy: https://plato.stanford.edu/entries/newton- stm/scholium.html#VI

* 2 Philosophy Now: Pinhas Ben-Zvi: Kant On Space: https://philosophynow.org/is- sues/49/Kant_on_Space

* 3 Leibniz: Third Paper (In Answer to Clarke’s Second Reply) in JJC Smart (ed): Problems of Space and Time (London, Macmillan 1976), p 89