Hegel’s Absolute is an Answer to a Paradox of Infinity as Incomplete And/Or Inconsistent

A strange formula for Hegel’s Absolute.

G. W. F. Hegel is a notoriously difficult philosopher, and one of his most difficult concepts is that of the Absolute. Many readings of it exist, as many as readers of Hegel. This reading will present Hegel’s Absolute as a solution to a paradox — one that occurs when we try to conceptualize infinity.

We can begin with a simple thought experiment: imagine two sets (collections of elements). One is the infinite set. Another is the finite set. Now, what is the relationship between these sets?

1. In one sense, we could argue that there is no overlap between them. The infinite set must contain things that are eternal, unchanging, unconditioned. And the finite set must contain things that are temporal, ephemeral, conditional. And so, they naturally are mutually exclusive.
2. In another sense, we could argue that the infinite set must contain the finite set. After all, if it is infinite, eternal, unchanging, unconditioned, then it must not be restrained — there can be nothing outside it, given that it is all there is. And so, the infinite set must contain the finite set.

The problem that arises here is simple enough, but crucial. The infinite of the first model is INCOMPLETE (there is a set outside it, uncontained by it, making it finite), and the infinite of the second model is INCONSISTENT (there is a space within it that is not infinite, making it also finite).

One way to solve this is to simply differentiate these sets: the first one is infinite insofar as its CONTENT is strictly infinite (the elements of the set are infinite); the second one is infinite insofar as its FORM is strictly infinite (the set itself is infinite). So far, so good. Not!

Hegel here encounters a problem. Can there be an infinity that is both infinite in content and form? Here, the antinomy becomes clear:

1. Once it is infinite in content, it must fail to be infinite in form. (The limitation to only elements that are infinite means that it is restricted from incorporating the elements which are finite)
2. Once it is infinite in form, it must fail to be infinite in content. (The unrestricted nature of the set means that it necessarily must incorporate also the elements which are finite)

Infinity, then, is always incomplete or inconsistent. And, therefore, non-infinite.

This problem of the insufficient infinity, this failure, is what Hegel tried to solve with his philosophy of the Absolute.

Being and Thought

Now, the most shaky step in the argumentation is demonstrating how this failure is exactly what Hegel was concerned with.

To begin with, we can substitute what we called infinite with what Hegel called ‘universal’, and what we called finite with what Hegel called ‘particular’. Naturally, there are two philosophical ways to establish the relationship between these registers, introducing chronological order:

1. We can go from bottom-up, with the universal being derived from the particular. That is, in a finite world, we can derive an idea of the infinite through abstraction, extrapolation, looking at the realm of experience and imagining what lies behind it, the suprasensory. In this view, it can be said that the finite is all there is, given that we are always barred from the infinite — it is the situation where the infinite is incomplete.
2. We can go from top-down, with the particular being a manifestation of the universal. That is, a given Idea appears at many times and places, any essence has many appearances, such that the infinite is omnipresent, manifesting itself in finite situations and entities. In this view, it can be said that the finite exists as a non-infinite subset of the infinite — it is the situation where the infinite is inconsistent.

These definitions seem to line up with Beiser’s interpretation that,

“according to Hegel, the universal is first in order of explanation, [and] the particular first in order of existence.” (BEISER, Hegel, p. 56, 2002)

In this way, we can see that Hegel accounts for the contradiction by introducing a difference, separate spaces for each view. Here, the order of existence (or being) accounts for the bottom-up view, deriving universals from particulars, of the infinite as incomplete. Meanwhile, the order of explanation (or thought) accounts for the top-down view, manifesting particulars from universals, of the infinite as inconsistent.

This is already a notion that separates Hegel from many other thinkers. There are many that favor the particular in all instances and many that favor the universal in all instances, making no difference between the orders of existence and explanation.

History

However, what exactly even is this difference (between being and thought)? In order to make sense of it, we only have to look at a famous passage:

“The owl of Minerva spreads its wings only with the coming of the dusk.” (HEGEL, Philosophy of Right, Preface, 1820)

This notion (in)famously introduces a temporal dimension to philosophy, by saying that it always “arrives too late at the scene”, can only accurately describe an epoch that has already passed. Yet, far from being a secondary concept to Hegel’s philosophy (say, incongruent with his attempt to precisely philosophize everything in the Absolute), this can actually be shown to be THE key feature of the entire Hegelian system.

1. Before dusk, when an event has not yet occurred or an epoch has not yet been completed, we are somehow barred from defining it properly. That is, from the perspective of something being not even in the future, but merely in the present, we cannot accurately describe it. We can describe its parts (particulars) and try to derive the whole (universals), in a bottom-up approach, but we are always barred by a certain incompleteness. This is the order of existence (or being), which can now be defined minimally as the register of the present.
2. After dusk, after an event has occurred or an epoch has been at last completed, we can finally formalize its full truth. That is, from the perspective of looking at the past, we can perfectly describe it. We can describe its parts (particulars) as manifestations of the whole (universals), we can retroactively show how things were destined towards a certain end in a top-down approach, how everything was a failed attempt to represent something infinite in finite terms, how it is defined by failure to achieve its own immanent universals, by a certain inconsistency. This is the order of explanation (or thought), which can now be defined as the register of the past.

The passage from incompleteness to inconsistency (the owl of Minerva setting flight) marks the singular moment of a historical break. ‘Dusk’ here is the name for a historical break, for an Event that posits its own presuppositions:

If — accidentally — an event takes place, it creates the preceding chain which makes it appear inevitable: this […] is in nuce the Hegelian dialectics of contingency and necessity. (ZIZEK, 2022)

This is how Hegel makes space for both infinities, the incomplete and inconsistent one: by placing them at different points in Time. Two contradictory notions can simply be true at different points in Time.

This is how Hegel’s Absolute solves the problem of insufficient infinities: a proper Absolute integrates Time itself into its formulation, so that it is consistent (if incomplete) in the present, and complete (if inconsistent) in the past!

However sound this argument may or may not be, it should clarify the position of Hegel as the so-called “Philosopher of History”: It is not that Hegel merely examined History and concluded that we were driven by and heading towards an Absolute Spirit realizing itself through Reason. Rather, the logic goes in the other direction: Hegel examined the conditions for an Absolute to exist and concluded by positing History as such.

Conclusion

In conclusion, from a thought experiment on infinity which results in a natural paradox, and a philosophical inquiry onto an Absolute which would preserve two contradictory truths, it is possible to develop the core of Hegel’s thought (though this may be very far from the intended and/or usual approach).

In the end, this is only one possible interpretation of Hegel — but it is one that accounts for the variety of contradictory interpretations of Hegel (from Beiser, to Kojève, to Pinkard, to Pippin, to Marcuse, to Hyppolite, to Žižek…) by showcasing how Hegel himself is a thinker of contradiction, opening up the space for unilaterality in inflationary and deflationary, metaphysical and non-metaphysical, theological and rational readings.

There are as many interpretations of Hegel as there are philosophers — and in this sense, Hegel can be understood as the ultimate Rorschach test of philosophy: from Marx, to Nietzsche, to Heidegger, to Deleuze… what each thinker finds in him reveals something about Hegel, but also quite a bit about themselves.