Intellect and Quantitative Knowledge

Intellect and Quantitative Knowledge: Runway

In the overall architecture of being, time adds a new feature of externality to the externality of space: externality as succession. Whereas space was an externality as co-existence, time is an externality in which existing things, external to each other and therefore separated from each other, also succeed each other.

This is a different feature of reality that, on the one hand, is more than spatial externality and, on the other hand, is based on the latter. To have a succession, you need something to succeed, and this ‘something’ exists as a spatial entity. 

From the three dimensions of time (the future, the present, and the past), only the present, the now, is the medium in which we encounter individual existences or concrete individuality. Such individuality lies at the intersection of a particular location in space, having thus its place, with the temporal dimension of the present. 

Although time has three dimensions (Hegel 1970, p.235), they can be met only inside of the (human) subjectivity since only here can we meet memory of the past and expectation of the future. Outside of this subjectivity, we meet time deployed as space, so to speak, in that, as with the transformation of the point into a straight line – which is the elementary expression of temporality – the spatial externality endures in time.

The consciousness of time cannot be met in nature, and the three dimensions of time can be given only within this consciousness. This consciousness of time is a new feature that adds to the spatialized time of nature. 

The now, as the fundamental unit of time, grounds the science of arithmetic. This idea is already present in Kant, who says that the general scheme of the category of quantity is the image or representation of the succession of the moments of time. 

The categories are the pure concepts of understanding in Kant. This is why Hegel also considers quantitative knowledge (i.e., the science of nature) a matter of the human intellect. Human intellect petrifies reality, suspending its flowing character.

The (spatial) magnitudes it sees everywhere are taken as multiples of fixed units, of those nows that are considered clear-cut moments in their isolation from any changeable content. 

Due to this petrifying of reality that the abstract moments of time, the nows as units, operate, Hegel, in his entire work, constantly criticizes the claim of human understanding and the (modern) science of nature to provide the ultimate knowledge of reality. For him, they disregard reality’s flowing and developing character, which therefore remains unquestioned in science and not understood in a culture based only on science. 

This is all the more visible today when we almost identify knowledge with science. This is why we have great difficulties understanding such topics as values, religion, or morality as domains of reality rather than merely results of subjective moods. 

For Hegel, numbers are, to a certain extent, only empty symbols, and their combination, however complex, cannot grasp the internal processual, i.e., transformative character of reality. This combination is devoid of internal reasons.

Scientific measurements and descriptions do not explain why something happens, i.e., what the reason is why something changes into something else. They only describe that change mathematically. 

Now, how can we understand change? What do we mean by change? Mathematical science cannot enlighten us concerning this question. It can only show us the regular character of change but leaves us ignorant concerning understanding what change is. 

Does physics tell us what a force is, such as the gravitational force? No. It only describes mathematically how it acts, namely according to the formula of the law of gravity. Science does not consider this force in its relation to the whole of reality: it simply takes it as if isolated from this reality and measures it. 

Indeed, reality can be seen as a tremendous combination of forces. Still, according to the spirit of Hegel’s philosophy, the description of this combination is not yet a real explanation because it has no internal necessity, being only the result of an indefinitely long series of accidents. 

You cannot understand something by explaining it as an accident. Even when you explain the fall of an apple as the necessary result of the action of the gravitational force, the latter is seen as the accidental result of how the properties of previously existing clumps of matter gave rise to this phenomenon when those clumps came together. Actually, after hearing that the apple fell due to the force of attraction exerted by the earth, you are as perplexed as before hearing this explanation. 

The apple’s fall is seen by science only as a spatial change. And this is why it is considered in isolation from the rest of reality, as something happening in the externality of space, where the contents of space are external to each other and also completely foreign to each other. 

Thus, ultimately, there is no relationship between the falling apple and the acting gravitational force, except a spatial one. You do not have here a broader explanation of how the falling of an apple is connected to other aspects of reality, like: what such a fall means for the apple tree, how it changes the tree, and what changes result from its falling. You do not get an understanding of the wider transformations attending the manifestation of gravity.  

You do not yet grasp change when one explains it to you as a change in spatial position – like the covering of the distance between the branch of the tree and the ground – and in temporal position, like the difference between the moment when the apple reached the ground and the moment when it started falling from the branch. 

What change really means remains foreign to you. Concerning the falling apple, you could as well move a metal ball from one place to another. In fact, since mechanics treat any real object as a point in motion, it ignores qualitative transformation and treats everything like a metal ball in motion, that is to say, like something that never changes and therefore is entirely inanimate. 

Real change or transformation is the process in which something both keeps its identity and changes it. In mechanical phenomena, you have the same identity, only changing its place. This is why it is the poorest representation of change.   


Hegel’s Philosophy of Nature, edited and translated by M. J. Petry, vol. I, London, George Allen, 1970.

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