“Accordingly, logic is to be understood as the system of pure reason, as the realm of pure thought. This realm is truth unveiled, truth as it is in and for itself. It can therefore be said that this content is the exposition of God as he is in his eternal essence before the creation of nature and of finite spirit.”
—Hegel, Science of Logic, p.29 (Gesammelte Werke vol. 21, p. 34)
A bold claim to make, I guess, but perfectly fitting in Hegel’s grand system uniting the determination of thought and the determination of being. If abstraction is that which is most concrete, then the logical movement of this abstraction is of utmost importance as the method which guides not only thought as it analyses itself transcendentally, but also being as such. Within the procession of abstract thought in progressing determination starting with the Doctrine of Being, through the Doctrine of Essence, up till the Doctrine of Concept, wherein it achieves full self-determination in the Absolute Idea, there is one particular notion which has provoked much debate, as it has itself been considered by Hegel as ‘the fundamental concept of philosophy’ – the True Infinite [Encyclopaedia Logic, sec. 95]. Before the appearance of the True Infinite, that is, in the most part of this noetic-ontic progression in the Doctrine of Being, there was a lack of any stable category which would self-sustain itself as being self-determining – that is, incorporating otherness into itself, for otherness throughout the Doctrine of Being is for Hegel the major source of determination of any particular finite thing. Many concepts are here involved, such as Something, Other, Constitution, Determination, Limit, Vanishing, etc., but this unfortunately cannot be the space in which they are explored in greater detail.1placeholder
Suffice it to say that the most general characterization of the logical progression from Pure Being, the first category of the Logic, to the True Infinite, is that successive stages achieve greater self-determination through sublating otherness into itself – realizing that the otherness is already inscribed essentially within the determination of something as something – something is a something by virtue of its difference to what it is not, and hence self-determination consists in the sublation of otherness within identity. However, the True Infinite is the first ‘stable’ category in the Logic, because all the previous ones, in order to achieve self-determination, depended on their Others, whereas the True Infinite is Being as such, as fully self-determined and ready to figure as the categories of Being-for-itself and the One to be employed later in the Logic [SL 132ff. (21.150ff)].
“The infinite is, in a more intense sense than the first immediate being [with which the Logic starts – A.K.]; it is the true being; the elevation above restriction. At the mention of the infinite, soul and spirit light up, for in the infinite the spirit is at home, and not only abstractly (…).” [SL 109 (21.125)]
We can see, therefore, how crucial the concept of the True Infinite becomes for all other parts of Hegel’s work – it is, so to say, the very abstract logic behind the activity of the Spirit itself. It bears probably the greatest importance on the question of the relationship of Hegel’s philosophy to theism, as well as in what way, if any, can we think of the True Infinite as Hegel’s revision and continuation of classical metaphysics.
Given my interest in these theological (or, in a more recently fashionable term: onto-theological) questions posed to Hegel’s philosophy, as well as, with respect to all previous content in the Logic before the True Infinite, wherein non-substantial, but rather negative determination of the Something is the universal rule, it struck me quite much when I was initially dealing with the latter that most of the commentators on the Logic thought of the True Infinite as purely immanent to the finite – that the True Infinite would be another way of calling the relationships of finite things in the determination of their quality. Quite simply, if this is so, the True Infinite would contradict the very aim that the Logic assigned to it as a category with ontologically completed self-determination, as it would still depend on transcendence as the other determining it as something, and therefore recede into the category of something which it was precisely meant to sublate. Instead, I shall here attempt to sketch in greater detail the progression in the Logic from simple finitude, through the Spurious (Bad) Infinite, up till the True Infinite. Then, I would like to compare the alternating determination of finite and infinite in the True Infinity with the analogous alternating determination of transcendence and immanence. This will be in order to demonstrate that the infinite Being-for-itself is for Hegel a model for the sublation of the difference between immanence and transcendence itself, not only on the ‘micro’ scale with respect to the debate between realism and idealism, but also in the ‘macro’ scale in the dispute between those who think that the True Infinite is ultimately immanent to the finite, and those who think that it is somehow transcendent from it.
From Finitude to True Infinite
We begin with the simple finitude of the third sub-section of Section B (under the same name) in the chapter on Existence. What we first need to explore is the nature of that finitude of particular determined things in the world. In contrast to much of previous substantialist, participationist, emanationist or monistic philosophies, for Hegel determination of the finite thing is essentially achieved through its non-being, rather than being or some Supreme Being (God). Furthermore, it is by reflection in their self-determination that finite things refer to themselves from outside of their being – they are limited and simultaneously exceed that limitation in the very act of posing it. In this way, particular things vanish and perish into one another as they determine themselves against those other things which surround them. Finitude is not granted its own ‘stability’ and determination through participation in or being grounded in some metaphysics of creation (whether theistic or mythological or both), but rather the taken starting point is the immediate condition of things which, in order to be determined, must self-differentiate between themselves through their limits, and hence, logically, be finite.
“The official claim is that the finite is incompatible with the infinite and cannot be united with it (…). The finite remains held fast over it against as its negative, incapable of union with the infinite, it remains absolute on its own side; from the affirmative, from the infinite, it would receive affirmation and thus it would perish; but a union with the infinite is precisely what is declared impossible. If the finite were not to persist over against the infinite but were to perish, its perishing, as just said, would then be the last of it – not its affirmative, which would be only a perishing of the perishing. However, if it is not to perish into the affirmative but its end is rather to be grasped as a nothing, then we are back at that first, abstract nothing that itself has long since passed away” [SL, 102 (21.117-118)]
This passage, apart from discarding the long-standing (fundamentally Platonic or Neoplatonic) stark opposition between finitude and infinity in which the former finds its grounding, speaks for the necessity of the transition from the finite to the infinite. If the nature of finite things is to perish infinity would be qualitatively separated from them (recall Kierkegaard’s ‘infinite qualitative distinction/difference’), then they have substantially two options. Either they keep perishing, turning into others which determine them forever and hence transit into an infinity of those limitations and perishings, this infinite conceptual and ontological life-death cycle. However, to transit into such infinity is the very thing that they are prohibited to do. Or, and this is the only standing option given the previous sentence, they can recede into sheer nothingness with which the Logic begins, which in itself is a category extremely poor in self-determination. So, it is the very nature of finite things, which determine themselves in infinite sequences, to recede into some kinds of infinity. But how is this process achieved in more detail?
Recall what I have just said about determination through limit and otherness. If every finite something has its own limit, which is its other, it also transcends this limit precisely by posing it. But we cannot say that it fully transcends it, because if that were so, there would be no limit and the thing would simply go on uninhibited. So, Hegel needs to invent a category of that which is outside of the limit, determines the thing, and yet is somehow not totally distinct from the thing, else it would not determine it as it is now. This category is restriction (in German Schranke), which has to be subtly differentiated from limit (Grenze). All things are limited by other things but posit their own restriction by attempting to negate this limit, overcome it and yet precisely being restricted by it. The limitation is the positing of a thing from its concrete limits, points in which it stops, so that in order to be what they are, to fully determine themselves, they would have to achieve the limitation which is the negative of their limit. But, once that is realized, the thing has its aspect of attempting to not be its limit which becomes what the thing actually wants to be, both is and is not – the next logical category – the ought. That what the thing should or ought to be both is and is not the thing – the former in a sense that the thing can only be taken as what it really is by what it ought to be, and the latter in a sense that the ought cannot be the thing precisely because it is that to which the thing strives in its self-determination, in its self-transcendence of reflection.
“What ought to be is and at the same time is not. If it were, it would not be what it merely ought to be. The ought has therefore a restriction essentially. This restriction is not anything alien; that which only ought to be is determination now posited as it is in fact, namely as at the same time only a determinateness.
(…), as “ought” the finite transcends its restriction; the same determinateness which is its negation is also sublated, and is thus its in-itself; its limit is also not its limit.
As ought something is thus elevated above its restriction, but conversely it has its restriction only as ought.” [SL 104-105 (21.120)]
We cannot at this point, sadly, discuss the moral aspects of this derivation of the ought from the very nature of the thing as self-determining, nor the comparison of such an approach with Aristotelian final causation. The ought is only important for us for its crucial role in the self-determining transition from the finite to the infinite and, in the end to the True Infinite.
This transition is achieved through the application of the problematics of the ought to those of finitude. Just above I have been speaking of this transition on the basis of the quote which Hegel wrote before introducing the ought. Now, after that, we can more fully understand the mode in which the finite reflects of itself and determines itself as the infinite. To say that the infinite is the ought of the finite is a gross simplification, but still captures the essence of what Hegel means by the transition. As we have seen the perishing and ending of the individual things constitute what defines them as finite determined by otherness. Where one finite thing ends, the other one begins, and, necessarily, if the ultimate determination of all finite things is not to be nothing, this process has to go on to infinity – there will always be another thing which will be the determining other to the thing. Taken as an aggregate of all those finite things therefore, the universal of finitude itself (and Hegel rather thinks universals in the Logic) has an ought, that towards which it constantly strives for, as the infinite itself.
This is the first sense of the infinite as Hegel conceives of it, a ‘mathematical’ one, being the infinite procession of finite things ending and beginning where the previous one has ended as their limits and determinations. As soon as one discovers that when taken as a whole, finite being is this ‘mathematical’ infinite consisting of an infinite number of particular things. There is not actual ‘finitude’ as a universal category defining all particular finite things, because if there is an infinite number of finite things, this category has to necessarily become the generic category of the infinite. We can already see here first signs of what I would like to argue for – the infinite is not immanent to the finite, but rather the opposite – we can only derive a finite being from the generic infinite set of all finite things which precedes it (especially given that Hegel always thinks the universal above the particular – recall his famous ‘truth is the whole’ maxim). But finite things are not, as if it were a reversal of immanence-transcendence distinction, transcendent to the infinite – they are rather the instantiation of the infinite as Spirit. It will become clearer, I hope, when we see how this simple infinite achieves fuller determination through Bad to the True Infinite.
How does the ‘mathematical’ infinite become what Hegel calls ‘Bad Infinity’? We have seen that finite being by its very nature turns out to be self-determining as an infinite being, because finitude as a whole can only be described as the series of all things vanishing into each other in their determination as Something and Other, and this process has to be unending because there will always be another thing which the thing we are now talking or thinking about will have to determine itself against. But Hegel makes a very interesting move then, in order to reveal the contradiction within the nature of infinite being and so provide for the transition to Bad Infinity. We have up till this point been thinking about the infinite as what the totality of finite being turned itself to be in the very beginning – the unending determination of finite beings, finitude ad infinitum. Hegel, however, now wishes to climb a step higher and see the ‘broader’ perspective in which this infinite being, which the finite being turned itself to be, can be grasped. What now is to be seen is quite a simple contradiction: if the infinite being is infinite because it is composed of an infinite number of moments, things, aspects of itself which mutually determine themselves against each other, end where the other has begun and begin where the other has ended, then it has to, itself as a moment determine itself against something else – it has to have a limit, which precisely is the finite. So the contradiction is that the infinite, which is the true reality of all that which is finite, namely that any particular finite being is just its moment, has itself to generically determine itself as Something with the finite as its Other. This is the ‘Bad’ or ‘Spurious’ Infinity, and it is bad precisely because it has, by wanting to achieve its own determination against the finite (note the very nature of the word: in-finite, German ‘Un-endlichkeit’), ceased being what it itself supposed to be, namely the very finite itself in its truth.
For Hegel, the Bad Infinity is the ultimate concept of the ‘understanding’ (which for him denotes both the lower level of human noetic activity beneath dialectical and speculative Reason, and is also a nickname for his predecessors whom he critically appraises – chiefly Kant). This is because, for centuries in philosophy, that what has been considered as Infinite was in deep contrast with the Finite, so that the distinctions between God and Creation, ideal Form and its instantiation, Ideal Being and its emanation, and, finally, as in Kant, the noumenal ‘Thing in Itself’ and its phenomenal manifestation. And, finally, as I want to show, the very opposition between immanence and transcendence. All those oppositions operate upon, in Hegel’s mind, a flawed logic of holding that the finite is dependent upon the infinite, in that the finite, when absolutized, turns itself to be Infinite, but it is simultaneously held to be in stark determinative contrast with the Infinite. Remember that for Hegel determination is always negative, as the negation of negation of the thing against which it determines itself, so any Infinite, God or noumenon which would stand ‘pure’ and ‘inaccessible’ in itself, amounts for Hegel for a poor and undetermined idea of the Pure Being, from which the Logic started. Given that presupposition, all the Infinites posited as completely transcendent to the immanent nature of finite being – that this finite being is their moment or is dependent upon them for its existence, or ultimately turns out to be such Infinity as absolutized finitude – they all simultaneously contradict themselves in depending upon finite being in order to determine themselves. Bad Infinity, as determining itself against the Finite, but simultaneously holding this Finite to be itself, or at least, that what depends on it and which ‘mathematically’ turns into it, enters into insurmountable contradiction.
But there is also another unresolved contradiction in which Bad Infinity lapses into, intimately related to the first. It is also pertaining to the nature of the Bad Infinity as determined against the finite. If the fact that the finite is already the infinite (as its moment) does not suffice to underline this contradictory nature of Bad Infinity, another such problem might be pointed out in that by the fact that Bad Infinity determines itself against its limit, which is the Finite, and cannot overcome it inside a greater unity, it actually remains a finite infinite – one which ends at a certain point because it is limited by the finitude from which it has to contrast itself. That what is posited as transcendent, usually collocated as something supreme or infinite, actually always already is limited by its own transcendence.
“The contradiction is present in the very fact that the infinite remains over against the finite, with the result that there are two determinacies. There are two worlds, one infinite and one finite, and in their connection the infinite is only the limit of the finite and thus only a determinate, itself finite infinite.” [SL 111 (21.127)]
The greatest paradox of God’s omnipotence in classical theism aren’t scholastic speculations about whether he can create a stone which would be too hard for him to pick up, but that he is limited precisely by his omnipotence, that omnipotence contradicts itself in not allowing him to lose or abandon it (that is why Hegel so much admires Christianity, wherein God does abandon his omnipotence, but feels that this is made only to a limited extent as God actually does not die on the Cross upon the classical account – that would be a heresy of so-called ‘patripassianism’). Similarly, if Something is ‘transcendent’ with reference to its Other, it simultaneously means that it is limited by its very transcendence – if it transcends its own transcendence, what is only left is that it returned back to immanence, from which, precisely by being transcendence, it predominantly differentiated itself.
The solution for this paradox of transcendence transcending itself in order to remain itself is the True Infinity. Rather than being opposed to the finite, it encapsulates the differentiation of the finite from itself in itself, in order to become the self-relating totality, subsuming all differentiation within itself. If determination is achieved through otherness, than there is no other logical way, for Hegel, to secure the very stability of being as being – it has to be static within its very own dynamism of differentiation and progressive determination. The static concept of ‘True Infinite’ can only actually be a denoting of the movement (conceptual, not temporal), of the Bad Infinite, through its limit and the negation of limit as restriction, proving itself to be the finite Infinite; and the finite, which, through its absolutization and the transgression of its own limit as restriction proves itself to be the Bad Infinite. The True Infinite is the moving self-transcendence of the Bad Infinite, which in itself is the self-transcendence of the finite. But this process of self-transcendence obliterates the very distinction between immanence and transcendence, as every immanence (world, matter, phenomenon) and every transcendence (God, form, idea, noumenon) is already part, moment and reflection of the self-grounding Whole, which is, as it appears subsequently in the Logic, Being-for-itself as such.
True Infinite Beyond Immanence and Transcendence
It has become, I hope, clearer at this point that the materialist or individualist readings of Hegel, which see the True Infinite as immanent to the finite, just the description of the self-determination and self-relationality of the finite, either finite being or finite subject, cannot be considered valid. Even if it is not, perhaps, explicitly denied by Hegel (the section on the Affirmative Infinity is, as any other part of the Logic, notoriously obscure), then it would follow logically from Hegel’s transition from finitude to the True Infinite. If, let us say, the True Infinite would only be a description of the character of material finite things, than this description by its very nature would posit its own ‘transcendence’ in the non-material and non-finite, so that the project of ‘confining’ the True Infinite into either materialism, reductionism, naturalism or, on the other hand, religious spiritualism and classical theism would inevitably find itself to be propelling the actually finite Bad Infinity instead of the True Infinite. The True Infinite has obliterated the central paradox that being unbounded is being confined by unboundedness, or that being unknowable is being already given to be known in this unknowability – and it has done so by defining itself as continuous movement of altering determination of finite and infinite over against itself – of transcendence coming back to immanence, and immanence rising to transcendence.
Therefore, when Hegel concludes his discussion of the True Infinite with a remark about the meaning of idealism, he does not connotate it in any way with the simple and finite transcendence of ideality over materiality, concreteness and finitude, nor of the immanence of this ideality of philosophy in materiality, concreteness and finitude, but rather of the infinite as being itself, which, by being a true expression of idealism, proves itself to be beyond the very distinction between idealism and realism.
“The claim that the finite is an idealization defines idealism. The idealism of philosophy consists in nothing else than in the recognition that the finite is not truly an existent. Every philosophy is essentially idealism, or at least has idealism as its principle (…). The opposition between idealistic and realistic philosophy is therefore without meaning. In thus calling the principle or the universal an idealization as we have just done (and the concept, the idea, spirit, deserve the name even more), and in saying then that the singular things of the senses are idealizations in principle, or in their concept, and even more so when sublated in the spirit, we must note, in passing, the same double-sidedness that transpired in the infinite, namely that an idealization is on the one hand something concrete, a true existent, but, on the other hand, that its moments are no less idealizations, sublated in it; in fact, however, there is only one concrete whole from which the moments are inseparable.” [SL 124 (21.142-143)]
If that what is ideal, or that what is transcendent (these are, of course, two different things) is only what there is in philosophy for Hegel, then does not this ideal (and, as I want to analogously put it, the transcendent) already represent that what is most real and concrete – the transcendence already that which is most immanent? The self-relation of Being-for-itself, which is the True Infinite in moving from determination of the finite to determination of the infinite and back again, is that what is both most ideal and most real – it is Spirit, which is neither transcendent nor immanent but transcendent in its immanence and immanent in its transcendence.
‘Truth is the whole’ as Hegel says elsewhere and the Whole, which is the Spirit modelled upon the conceptual skeleton of the True Infinite is not in any way transcendent from its moments, nor simply immanent in them, but is the very structure of transcending and immanentizing itself in those moments. If it were simply transcendent, it would have to determine itself negatively from the immanence of its finite moments, which as we know leads back to a ‘finitized’ transcendence, while if it were to be purely immanent in its moments than there would be nothing else than these purely finite moments, which in turn leads to the absolutization of finitude and, in the end, its turning back to another Bad Infinity. The True Infinite is the ‘third’, the Spirit, the becoming of the dyad – the becoming of immanence into transcendence and the becoming of transcendence back to immanence – the determination of Spirit is alternatingly in its immanence to and transcendence from its moments. It is in this way that the Spirit moves and in this movement, becomes through various modes of representing its own functionality – whether morality, ethics, art or religion, until it finally makes itself most conscious of its own being in speculative ontology of the Logic – a reading of the mind of God.
Works Cited
Hegel, G.W.F., The Science of Logic, trans. George di Giovanni, Cambridge University Press, Cambridge 2010.
Hegel, G.W.F., Encyclopaedia of the Philosophical Sciences in Basic Outline. Part 1: The Science of Logic, ed. and trans. Klaus Brinkmann, Daniel O. Dahlstrom, Cambridge University Press, Cambridge 2010.
I recommend Antonio Wolf’s essay How to Pull an Ought from an Is: Hegel’s Being to Ought in Issue 44 of this magazine for a more detailed discussion of the procession of the Logic up to Finitude and the Ought. In some ways, this essay picks up at almost exactly the point where Wolf’s ended. Another of his essays which pertains to the a similar problematic is Hegel: We Are All Idealists, Just the Bad Kind (Issue 07).