Measure, or Hegel’s theory of destruction

There is a justly famous subsection in Hegel’s Logic where he describes “the sudden conversion into a change of quality of a change which was apparently merely quantitative” (p. 335). This subsection, as far as I know, contains the clearest expression in his writings of the famous dialectical leap (or Umschlag) from quantity into quality. Below I'd like to offer a few reflections on the relevance of this idea for some present-day discussions, e.g. climate change and the idea of emergence.

The relevant passages occur in the context of Hegel's discussion of what he calls “measure”. According to Hegel, everything that exists is determined by the magnitudes, or quantities, of the things that constitute it. When a particular magnitude becomes defining for the entity in question, it is called measure. For example: a dwarf that grows above a certain size is no longer a dwarf. A piece of sandy land needs to exceed a certain size before we call it a desert. Hot days need to continue with a certain regularity before we can speak of climate change, and so on. The size or magnitude (a quantity) is thus part of what defines the thing (a quality). As Hegel writes, the specific quantity (or quantum) “is now the determination of the thing, which is destroyed if it is increased or diminished beyond this quantum” (p. 333f). 

According to Hegel, measure is a paradoxical. This is because we usually can’t find anything in the concept of a thing that pinpoints the exact quantitative limit where a qualitative change must occur. This makes us think that we can vary the quantity without affecting the quality. A forest needs to have a certain size in order to be a forest, but it will surely remain a forest even if we cut down one tree. A heap remains a heap even if we remove a grain of sand from it, and a hair pulled from a person’s head doesn’t make the person bald. Yet, obviously, if we keep cutting, removing and pulling we will eventually arrive at a point where the forest and heap will disappear and the person will be bald. What Hegel describes here is the so-called sorites paradox (from the Greek word for heap).    

Hegel concludes that:

... the destruction of anything which has a measure takes place through the alteration of its quantum. On the one hand, this destruction appears as unexpected, in so far as the quantum can be changed without altering the measure and the quality of the thing; but on the other hand, it is made into something quite easy to understand through the idea of gradualness. (p. 334f)

This passage is remarkable for two reasons. The first is the range of Hegel’s claim. He claims that anything can be destroyed through quantitative alterations (this is the only possible interpretation since “everything that exists has a measure”, p. 333). Hegel is clearly aware of the gravity this lends his statement. He goes out of his way to argue that the examples he has given about heaps and baldness “are not a pointless or pedantic joke” (p. 336). Instead, they point to a paradoxical quality that adheres to everything that exists. There’s a brittleness to things which we cannot grasp if we focus only on their quality, on the way we understand them through concepts. The destruction of the State or of great fortunes are two further examples:

Quantum... is the aspect of an existence which leaves it open to unsuspected attack and destruction. It is the cunning of the Notion to seize on this aspect of a reality where its quality does not seem to come into play and such is its cunning that the aggrandizement of a State or of a fortune, etc., which leads finally to disaster for the State or for the owner, even appear at first to be their good fortune. (p.336)

This is a magnificent passage. That it comes like a bolt out of the blue in the midst of Hegel’s long, notoriously abstruse and seemingly apolitical discussions about quantity and quality only makes it more impressive. No wonder his idea of the transformation from quantity to quality later came to inspire hosts of revolutionaries!

Secondly, Hegel points to an interesting curiosity. The destruction is always unexpected, he claims, and this despite the fact that it is quite easy to understand what causes it. Strangely, it’s not because of ignorance that we are surprised by the destruction of a State or a fortune. On the contrary, we are surprised because the concepts we use tell us that small quantitative changes in things won’t affect their quality. We know that removing one grain of sand from a heap won’t make the heap disappear, because that’s part of the concept of a heap. That’s why politicians and capitalists, and others too, are justified in thinking that a little more aggrandizement won’t hurt.

Who can avoid thinking here of global warming? We all know that releasing greenhouse gases into the atmosphere is bound to cause global catastrophe, yet we go on thinking that “a little more won’t hurt”. And we are quite correct in thinking so. Surely, it can’t possibly make any difference to the global climate whether I choose to walk to my job today or to take the car. Similarly, it doesn't make any sense to claim that any particular molecule of CO2 is decisive in causing global warming. It’s precisely because we are so irrefutably correct that we’re in for a surprise when we realize that the catastrophe is here. To put it differently, we can’t stand with a measurement instrument in hand and say: now the catastrophe begins. What happens is rather that, when the dialectical Umschlag finally occurs, we realize that the catastrophe has been going on all the time, and that we were living in its midst even when we still thought that things were fine. The Umschlag brings with it a shift of perspective from which it becomes possible to project the origins of the catastrophic process far back into the distant past. To awaken to the catastrophe of global warming is thus to realize not only that the catastrophe is here, but that it has been unfolding ever since the industrial revolution first brought steam engines into the world. It's not just that quantitative changes give rise to qualitative ones; there is also an opposite process, through which the qualitative shift produces a certain version of the past which tells us which quantitative processes should be deemed relevant and important. That's why the awareness of catastrophe often seems to include the realization that the catastrophe isn’t new. The catastrophe started already when we cut the first tree, removed the first grain of sand, and plucked the first hair.

The economy is perhaps an even better example of how changes both surprise us and don’t surprise us. I’m not thinking here of the constantly recurring speculation bubbles, which certainly surprise us so often that they no longer surprise us, so much as of the ideology of endless exponential growth. Mainstream economics has so far failed to make sense of such growth, which clearly leads to absurd consequences if extrapolated far enough into the future. What seems to be missing in the models used in economic theory is that they fail to acknowledge that their concepts are defined by a “measure” which sets limits to the magnitudes that they can comprehend. If we think that two per cent annual growth every year is good, but that endless exponential growth is an absurdity, then we clearly have a problem in how to relate quantity to quality. To be more precise: our entire economy is built around the sorites paradox.

At this point, I think it’s not far-fetched to link Hegel’s ideas to present-day discussions about emergence. Emergence is what occurs when it is possible to discover a quality in the whole that doesn’t exist in the parts. In many well-known examples used to illustrate emergence in the field of complexity theory, the emergent quality hinges on quantitative change. Crowd behaviour, for instance, arises from a quantitative increase in the number of people. Mobilization processes in social movements, the diffusion and establishment of new technologies, or the way size impacts organizations are other examples. 

Yet when we look closer at the idea of emergence we discover an ambiguity related to how it brings together qualitative and quantitative change. On the one hand, emergence is a causal process, in which a macro-level phenomenon results from complex, interlocking processes originating on the micro-level. On the other hand, emergence is also the result of a conceptual Gestalt shift, or shift in perspective, which in itself says nothing about causality. As an example, we can return to the heap of sand. The heap isn’t “caused” by the grains of sand in any ordinary sense of the word. For instance, there is no temporal sequence such that we first have grains and then a heap. If we dump a load of sand from a bucket, the heap exists from the start. In many discussions about emergence, it seems to me that a clearer distinction between the causal and the conceptual is needed. Exclusively focusing on the causal aspect of emergence easily leads to debates about directions of causality – whether it can only be from micro to macro, or the other way round or between macro-entities as well. While these discussions are important enough, they shouldn’t obscure the fact that causality alone can never explain emergence. Emergence also depends on our ability to capture changes in quality. Without that ability, a dwarf that grows in size would simply be a big dwarf, not something qualitatively different. Nothing would be surprising to such thinking, since nothing qualitatively new would ever happen. On the other hand, exclusively focusing on the conceptual aspect would be equally bad, since it would make us blind to the forces that undermine our concepts, to the way they are “open to unsuspected attack and destruction”, to quote Hegel. Without understanding those forces, we’d deprive ourselves of means for understanding change. All we would have would be one surprising change after the other.

To capture both the causal and the conceptual side, I think it is worthwhile to return to Hegel and to how he describes the transformation of quantity into quality as a process that paradoxically leaves us both surprised and not surprised at the same time. What Hegel seems to be saying is that quantitative processes – that may well involves causal mechanisms, such as the greenhouse effect – compel us to conceptual shifts that allow things to appear in a qualitatively new way. The compulsion here, however, is not of a causal nature in the sense of a law-like regularity or automatic reflection. The compulsion arises as a response to surprise, just as when we suddenly realize that the heap of sand has disappeared. This is significant, because it shows that Hegel is not an idealist in the sense that we can disregard experience. As I’ve argued elsewhere, his idealism consists in his belief in the ability of thought to retrospectively endow experience with meaning by shaping it into a conceptual totality. 

The question with which I would like to end my reflections today is this: doesn’t Hegel’s remarks on the subversive nature of quantitative change also provide an opening for idealist self-criticism? Even if Hegel opens up thought to experience, his understanding remains conceptual and organized around qualitites. But an important lesson from his discussion about measure is that quantitative changes are radically subversive. No matter how correct and justified we are in clinging to the quality of the world as we comprehend it, quantitative changes continually undermine and destabilize it - precisely because they takes place “below the radar” of conceptual thinking.


Reference:

Hegel, G. W. F. (1969) Science of Logic (tr. A. V. Miller), Oxon: Routledge.