Sublation: Negation of Negation

“To sublate and being sublated (the idealized ) constitute one of the most important concepts of philosophy. It is a fundamental determination that repeatedly occurs everywhere in it, the meaning of which must be grasped with precision and especially distinguished from nothing. –What is sublated does not thereby turn into nothing. Nothing is the immediate; something sublated is on the contrary something mediated; it is something nonexistent but as a result that has proceeded from a being; it still has in itself, therefore, the determinateness from which it derives.”

—The Science of Logic, Cambridge trns.

With Hegel, nothing is more unique and important than the concept of sublation, a most sublime concept which is spoken of in many a manner, yet which few treat with the extensive depth it deserves. The concept is certainly simple, yet its simplicity is as all things Hegelian a murky depth. Sublation is spoken of in a few ways: negation of negation, absolute negativity, and negative unity.

We have all heard of the transcending nature of what sublates over what is sublated, of its ‘synthetic’ character of uniting what is opposed, of being the positive moment of the negative, but what does all of this really mean?

Contents

Abstract Negation
Static Negation
Negative Unity
Dynamic (True) Negation of Negation
Self-Reference

Inner Structure of Sublation

One of the most unique aspects of Hegel’s concept of sublation is its explicit reflexivity,  i.e. its self-reflecting, self-referencing, and self-operating nature. It is necessary for one to have a notion of the logical process of Hegel’s concepts to understand what I shall mention here, so if you do not I advise you to read about the method first.

Sublation’s inner structure is revealed in a few places explicitly, and it is there where I draw the proof of what I am about to lay out here. It must be warned that this at first is presented as a static image, but sublation is no mere motionless image. As Hegel notes in a few places, the Concept is a peculiar contradiction as a motionless movement.

The Other

In the Science of Logic’s second chapter there is an exposition of the concepts of the other and something. With the ‘other’ in absolute form we get the very first explicit concept that works in self-reference and operation. The other is in itself the other of the other to which it is other. Thus, we first have this relationship which appears on what may be considered a ‘flat plane’ of relation:

{other}{other}

This is not yet sublation. Sublation occurs when the first ‘other’ is thought through and becomes concretized by conceiving it in its fuller truth, that it is not simply ‘the other’, but that it is truly the other of the other, i.e. the other which is other to and through the other. The explicit positing of this negative relation of otherness to itself is the moment of self-transcendence, of unification, and of positivity.

{other{other}}=Something

The first other which posits itself as ‘the other of the other’ (something) subsumes the second other as a mere moment of itself. This is revealed to be a bit of nonsense, however, when we realize that there is no way to really privilege one other to another as the other which returns to itself. The way it is written and said reveals the impossibility of such privileging: ‘the other of the other’ works both ways. Something is not one of these others; it is in fact the entire structure and movement of self-otherness.

When this negative relation of otherness is taken as being, it is revealed as the positive form. The other which is other to the other is what Hegel terms something, the at-face positive concept which we normally think does not point beyond itself and is simply the self-identity of beings. Something is through not being the other to which it is other to and is impossible without it. Something is ‘the other’ which has concretized itself by explicitly positing ‘the other’ to itself as a necessary moment of itself even if only as a negative relation to this other, i.e. the second other is expelled from the first other and then negatively reflected from and posited as an inner moment of something; thus, the other as something is otherness in a negative unity. When the concept is thought through, we recognize that the other to something is itself something and it becomes explicit that something is in negative unity with itself, thus falling apart once again and engaging the logic of otherness anew in relation to limit.

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Abstract Negation

When this relation is taken as a form merely in this flat ontological negative side-by-sidedness, we fall into abstract negation of negation, i.e. of a merely supplanting or rejecting negation. Each negation simply is as a negation of the other negation it is excluding or by which it is excluded. It is negation in merely one-sidedly negating. With this kind of negation of negation, ‘the other’ is other to ‘the other’ only as a sequence of one other taking the place of another. The first other is negated by the second, and this second is negated by the first. One other is replaced by another in an endless chain of supplanting negation. One negation is negated by another negation, and this latter is itself negated by yet another and so on. In this flat and momentary negation of negation, it is not the case that negation as such is negated; it is only perpetuated in an endless return towards a privileged abstraction.

When we cease treating moment by moment, however, we still have a static structure:

{negation}{negation}

This reveals one side of the negative unity which we see in sublating terms.

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Static Negation of Negation

In the doubled negative unity of ‘the other’, we can simplify the relation to a concept prior to it—the concept which we are really interested in here: negation. The concept of something is the being of this form of relation:

{negation{negation}}

The ‘other’, taken as the moment of negation, is often taken as the negation of something else and as such it does not normally occur to us that in some way a unity must be negating itself if there is any negation going on. Otherness, however, itself requires nothing else to refer to in order to be intelligible as otherness. An other is other to an other—it is a negation that merely negates what negates it and as such engages a structure of doubled-negation within which it exists as merely negating itself as one and the same concept, for it is otherness itself which negates otherness.

The other which the other negates is its own conceptual inner content, produced by its own conceptual movement in merely being the concept that it is. This is the origin of the negation of negation, of negative unity, of  absolute negativity. Otherness as such (treated as absolute) is self-otherness—negation in truth must be self-negation. When concerned with an absolute, the only possible and actual relations and operations are self-relating. Here I designate what is shown so far as merely static in that it shows only the self-containing structure, the doubledness, the reflection, of negative unity. Merely seeing this structure, however, is not all that Hegel means by it.

This relation of negation to itself does not explicitly appear in other prior concepts except for Becoming, where it is only partly explicit if one catches it. Becoming must become and thus paralyzes and vanishes itself as two totalities of itself in Coming to be and Ceasing to be, but in order to grasp that each moment of Becoming is itself a totality of Becoming we must take the step of subjectively reflecting on the moments to see that they are also their opposite at one and the same moment when seen in their total movement and relations. Ceasing to be of Being is at once the Coming to be of Nothing, and Coming to be of Nothing is at once the Ceasing to be of Being. As such, Becoming is the negative unity of structural reflections regardless of which one we privilege: either Coming to be is in negative unity with itself when faced with its opposite or its inverse is so. We may even playfully generate a variety of term relations such that Coming to be is the Ceasing to be of Ceasing to be or Ceasing to be is merely the Coming to be of Coming to be, for to Come to be is the Ceasing to be of what has Come to be prior. All are merely an explicit show of the presence of this negative unity of these categories.

With ‘the other‘, we need not make a further step to see the reflection; it is already explicit. This static negative unity is still an abstract form of negation of negation because it is only the motionless inner structure of negative unity, but there is a second and more true form of negation of negation which involves precisely the unity of the negations as the dynamic self-transcending movement and totality of these negations in their inseparability.

Negative Unity

Negative unities are very simple: simply see the concept of ‘the other’ as it immediately is reflected against itself. Something is the negative unity of ‘the other’ with itself, i.e. it is this necessary unity of mirrored opposites (no one expects the opposite of otherness to be otherness, strangely). Something, as the totality which is other to the other, has positive being as and through the negative unity of otherness. Were this otherness not there to be repelled, to be negated, to be othered, something could not exist at all. Negative unities, because they are unities, are the universal through which moments subsist, but likewise the terminology reveals the universal’s dependence on its inner moments (particularities). Perhaps a more concrete example shall do better.

Universals As Negative Unities

Now because the pure essentiality of things, like their difference, belongs thus to reason, we can, strictly speaking, no longer talk of things at all, i.e. of something which would be for consciousness merely the negative of itself [i.e. consciousness]. For to say that the many categories are species of the pure category means that this latter is still their genus or essence, not opposed to them. 
—Phenomenology of Spirit, §236 Inwood trns.

Regarding the essence of things, as the unitary factor of differentiated appearance, there is nothing to speak of as something when essence is considered as non-opposed to its differentiated appearance in the same manner that Being is considered as non-opposed to beings. Where there is no opposition, there is no way to talk of things because there is no basis of differentiation in this consideration. Beings are, and appearances are moments of essences. The relation of genus or universal to their species/particulars/individuals cannot be of a typical sense of opposition.

But they [the many categories] are already something ambiguous, which at the same time has in itself otherness in its plurality in contrast to the pure category. In fact, they contradict the pure category by this plurality, and the pure unity must sublate them in itself, thereby constituting itself as negative unity of the differences. But, as negative unity, it excludes from itself the differences as such, as well as that first immediate pure unity as such, and is singularity; a new category which is consciousness as excluding, i.e. consciousness for which there is an other. 

With regards to concepts as species of a universal Concept as genus or essence we likewise may find no way to speak of the Concept if we conceive it as non-opposed to the differences. To speak of a universal in these situations, we can only speak of a negative unity in the manner that the unity only exists in this differentiation. Something is a negative unity of otherness, and in this difference as such the universal is not part of the opposition of what is different, for what is different in something is the otherness, but this otherness opposed to itself is also identical. The unity of something is not a pure immediate unity such as we think we find in ‘pure Being’; it is a self-mediated differentiated negative unity. With negative unity established in the Phenomenology, we have opened for us a new categorial relation, singularity, wherein we do not simply have otherness as such, nor do we have mere others; we have this and that other.

Singularity is the transition of the category from its concept to an external reality, the pure schema which is both consciousness and, since it is singularity and exclusive unit, the pointing to an other. But this other of this category is merely the other first categories, viz. pure essentiality and pure difference; and in this category, i.e. just in the positedness of the other, or in this other itself, consciousness is equally itself. Each of these diverse moments refers to another moment; but at the same time in them we do not get to any otherness.

With singularity, “external reality” is achieved because otherness becomes fully actualized and does not remain as a merely formal generality. With regards to categories—the most basic concepts of thought—their other is another category which partakes of the form and content of the system of the one to which it is other. Consciousness takes the world as its other, but this world is the world of consciousness and merely affirms it in every encounter. Whatever moment of existence we investigate reveals that it is not an ultimate other which is in true independence from us; all is partaking of one differentiated unity—negative unity. Hegel closes the paragraph with one of the many descriptions of the true universal:

The pure category refers to the species, which pass over into the negative category or singularity; this latter, however, refers back to them; it is itself pure consciousness which in each species remains to itself this clear unity with itself, but a unity which equally is referred to an other, which, when it is, has vanished, and when it has vanished, also regenerates itself.

Dynamic Negation of Negation

True Sublation & Absolute Negation

At the base of all these determinations there lies the negative unity with itself. In all this, however, care must be taken to distinguish the first negation, negation as negation in general, from the second negation, the negation of negation which is concrete, absolute negativity, just as the first is on the contrary only abstract negativity.
—Science of Logic, §21.103

In the category of ‘the other’, we find the simple explicit truth of what Hegel means here. In the depths of the Concept, we find this self-otherness—this negative unity of the Absolute with itself. This relation is no mere relation, however; it is itself the process of absolute negativity.

The difference between abstract negation of negation and absolute negation is simply the difference between the frozen image of negation’s externality to itself. While in abstract finitized form, it looks like this:

{negation}{negation}

In infinite speculative form, it looks like this:

{negation{negation}}

However, it is impossible to diagram the true negation of negation because it is a moving negation which is only apparent in its fullness in the thinking of the concepts. Negation in the absolute form is simply negation in self-operation. In self-operation, we find already explicit self-relation, self-reference, and inner reflexion. The Absolute relates only to itself in relating to another, negates only itself in engaging negation, finds the other of itself within itself, and as such only overcomes itself in limiting itself. This negation cannot be a simple side-by-sidedness of opposites as if it could be in any way external to the Absolute, it must be an inner negation. The first negation, abstract negation, logically reveals the difference in the Absolute as particularities in mutual negation—as others that seem external and indifferent. The second negation is not negation of a particular negation, but it is the negation of negation as such, i.e. the overcoming of the very category of negation, of the cancellation of the illusion of abstract separation, through simply running through the logic of negation as absolute. Sublation as negation of negation is categorial self-negation: other of the other, restricted restriction, the ought of the ought, finitized finitude, et cetera. When a concept runs itself through its own logic, it transcends its limitations and engages the process of self-sublation.

Negation in negating itself also negates the otherness, the independence, of the negation before it. It not only is the case that it has found itself as a reflected other like itself—{negation}{negation}— but in being capable of negating this other as other, it shows that this other is in fact one with itself and mere moment of it—{negation{negation}}. Absolute negation is thus negation which brings what is negated into itself and does not destroy it.

Self-Sublation

In Becoming’s short section in the Logic, Hegel already notes self-sublation as what is in play. Ceasing and Coming to be self-sublate, put themselves into explicit inner relation to their opposite other and negate themselves into this other: Ceasing to be is Being vanishing to Nothing and Coming to be is the inverse. In these terms, Being and Nothing are already sublating themselves in relating to their opposite.

“This coming-to-be is the other direction; nothing goes over into being, but being equally sublates itself and is rather the passing-over into nothing; it is ceasing-to-be. –They do not sublate themselves reciprocally – the one sublating the other externally – but each rather sublates itself in itself and is within it the opposite of itself.” [emphasis added]
—§21.93

Sublation, as is clear here, is not something that comes externally such that we may say our mouths sublate the orange that we eat, that the car sublates the motor within it, or that this sublates that. The ‘inner’ is not sublated by the ‘outer’ in an external fashion, but instead finds its determination as this very outsidedness developed in its absolute form— the outside of the outside. Ceasing and Coming to be are a unity of Being and Nothing, but even more they are also a unity with their opposite on their own conceptual level. In merely being themselves, they already explicitly tell that they have also passed and will pass into their opposite.

Self-Reference

This immanent turning back, as the sublating of finitude – that is, of finitude as such and equally of the negative finitude that only stands opposite to it, is only negative finitude – is self-reference, being. Since there is negation in this being, the latter is existence; but, further, since the negation is essentially negation of the negation, self-referring negation, it is the existence that carries the name of being-for-itself.
—§21.138

Sublation, as the immanent turning back, is this self-reference, relation, and operation of a term to itself by othering itself only to find itself in this other and thus reflect right back. Finitude is sublated when it operates its own logic on itself, thus making finitude truly finite. At first, we have only {finitude}{finitude}, the negative finite, and its abstract negation against the spurious infinite which is itself only a repetition of the structure of finitude. With sublation, we have {finitude {finitude}}, the infinite as the finite overcoming itself by engaging its own logic of finitude and incorporating its ought as well as restriction. It is then finitized finitude. Thus, it transcends its limits in operative self-reference, i.e. in merely fully being itself, the finite necessarily engages the infinite.

The finite, over and beyond itself, falls into the infinite, but that, over and beyond this infinite, it equally finds itself born anew; hence, that it rejoins itself there, as is also the case for the infinite – so that this same negation of negation results in affirmation, a result that thereby proves itself to be their truth and point of origin. In this being which is thus the ideality of the distinct moments, the contradiction has not vanished abstractly, but is resolved and reconciled, and the thoughts, while left intact, are also brought together. Here we have, in a graphic example, the nature of speculative thought displayed in its determining feature: it consists solely in grasping the opposed moments in their unity. Inasmuch as each moment shows, as a matter of fact, that it has its opposite in it, and that in this opposite it rejoins itself, the affirmative truth is this internally self-moving unity, the grasping together of both thoughts, their infinity – the reference to oneself which is not immediate but infinite.
—§21.139

Sublation has a process and structure of self-reference. In abstract negation, we have {negation}{negation}, the relation in its mere self-repulsion from an ‘other’ which is just as actively repelled from the first—a mere one-sided abstract negativity. Negation refers to negation, i.e. refers to itself as if referring to an external other. With regards to the finite as such, for example, it is only finite in face of another finite opposite of it—a finite which the understanding misunderstands and mistakes as the infinite opposed to the finite. The relation of {finite}{finite} is the one of the necessary ways finitude is intelligible, i.e. it is finite precisely because it limits and is limited; thus, the finite is itself in reference to itself. This is misunderstood when this reference of one to the other is taken as if the reference was not immanent, but only externally reflective. With the other, it is only the absolutely negative when it is taken that it is indeed the other of the other, and that this is its own content.

This reference is not the analytic emptiness of A=A, but instead is the true self-reference of conceptual reflexion. The finite, in and of itself, generates its own finitude and ascends in this process as the infinite by positing its own limit, its restriction and ought. The Infinite is this process of dissolution and reconstitution of finitude. The full meaning of this is something to be experienced in the Science of Logic.

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