Space and Negativity

Space and Negativity: Steps

In Hegel, self-externality of space is only a logical condition for everything that exists. As logical, it concerns pure possibility and not reality. Space is everywhere opening itself into other self-external spatial contents. 

The difficulty of understanding Hegel in his explanations concerning nature is that we tend to understand the concepts about which he speaks as realities, whereas he takes them in their pure conceptuality, that is to say, in their possibility. For space, Hegel says in this respect: ‘Here is not yet place; it is merely the possibility of place.’ (Hegel 2007, p. 224)

This is how the infinity of space must also be understood: there are no spatial limits because the boundaries of space are possible and not real. As such, they constantly open toward other spatial possibilities. Self-externality is a condition of space. However, it is not a condition that we discover in experience but an a priori condition, in an ontological and not epistemological sense.

In other words, space will always actualize itself as self-externality because this condition belongs to the Notion of space, to that transcendent entity which, in Hegel, is creating reality. The self-externality of space is the ultimate feature, the most elementary property of reality, the element of knowledge from which I must necessarily start in my undertaking of knowing reality.

Trees, animals, grass, colors, cars, planets, galaxies, black holes: all these, together with their contents and apart from all the other properties that they have, are also always external to other things, alongside other things. (Material) reality does not overlap with, but disposes itself alongside, other real contents. 

We can understand Hegel’s approach if we give up imagining space as a given, objective reality existing apart from us. Space has no reality but is constantly created by the Notion as self-externality or as something capable of sustaining the material world as we know it. 

When the point is posited in space, it is not as if the point emerges from that pool of possibility which is pure space, but the point is rather given in opposition to pure space. You must already have the point which, thereafter, you can relate to space as pure self-externality. In relation to space, the point is a reality, so to speak, and no longer a pure possibility as the pure space was. 

This is why it is a limit of space: the point is in space, and you cannot put another point over that existing point. The point is an abstract reality but, in comparison to space, still a reality. It is the mark of that thought which says: here, I cannot go further. This limit or border of space is, therefore, a negation of space’s self-externality: the point stops this potentially endless opening of space into smaller and smaller places or ‘heres.’

But, again, the ‘point’ is not a reality but a concept, that is to say, a possibility of human understanding, of our intellect. From this perspective, space is not an infinite pool or box of points lying alongside each other. If you think that way, you transform space from a possibility into a reality. 

As with the Roman Empire necessarily transforming into a Christian Empire – where you think necessity starting from the existing Christian Empire and looking back for the logical condition that made that transformation possible, namely Jesus’ appearance in history – you must not think that space is a multitude of points but that the multitude of points requires the thought condition of space. 

In other words, as everywhere in Hegel, you must proceed from what is later toward what lies earlier, and thus you do not deduce the point from the space but the space from the point. Because everywhere I look I see things existing beside each other, I must think of space as self-externality. (And not because space is an a priori intuition or an order of things I see things apart from each other.)

The science of geometry speaks about the ultimate elements of space: points, lines, planes, etc. We have seen that points negate the never-ending self-externality of space. In the same way, the line must negate the point. This ‘negation’ must not be thought of as if the line ‘annihilates’ the point. It is a logical negation, i.e., it says that the line is something different from the point. But this difference is the smallest possible one.

Here, the point is not compared with a car, for example. The number of differences between a car and a point is tremendous: the point has no dimensions. Its sole determination is that it is a limit of space, namely something that stops the never-ending separation of space into smaller and smaller distances.

On the other hand, a car has an innumerable number of properties: it is white, it is hard, it has a spatial shape, and it is made of steel, glass, rubber, and plastic. All the latter have their own properties. The car also has a weight, someone makes it, it is merchandise, and so forth.

Thus, the number of properties is vast in comparison to the simplicity of the point. Of course, you can compare the point to a car (or anything else), but you would get lost in your enterprise. 

Hegel’s approach is to find the elementary conditions of our knowledge and then to add, step by step, the next simplest conditions to them so that, in this series, the later conditions can be understood through the previous ones.

Thus the straight line is, as one might say, a point in motion or an entity that has only the dimension of length, whereas the point was devoid of any dimensions. 

The same is true about the plane: the plane is a new entity that, unlike the line, has not only one dimension, length – as the straight line – but it has two dimensions, length, and breadth. The point, the line, and the plane are already determinate entities compared to space. This is why they are already qualities, ways of being, and not pure or indeterminate possibilities as space was. 

Hegel then interprets all the geometrical shapes as differing from each other through a property that is added each time to a simpler figure.   


Hegel’s Philosophy of Nature, edited and translated by M. J. Petry, volume I, Routledge, London and New York, 2007.

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