C. (Qualitative) Infinity

1. Finitude and Infinity

Existence is determinate; and determinateness posits itself as negation and restriction through this, that as a determinateness which is within itself it at the same time goes out beyond itself, and refers itself to itself as to its negation. In this way existence is not merely determinate but limited; finite, and it is not merely finite, but it is finitude.

Insofar as we say of things that they are finite, what is understood by this is not merely that they contain a determinateness, — for quality can be taken as determination or also as reality, — but that it is not being, rather non-being as restriction, that makes up their nature.

But what is determinate is finite only in the ought; that is to say, insofar as it goes out beyond itself as beyond its negation. The finite is negation insofar as it is negation to itself, refers itself to itself as to non-being, insofar therefore as the restriction is by it just as much sublated. It is, namely, the limit insofar as this makes up being-in-itself, or the determination, that is to say, just as much insofar as it refers itself to itself, and so is equal to itself. But in this reference of negation to itself consists the sublating of the negation of it, or of its inequality. Determinateness is therefore negation and finitude only insofar as at the same time there is present in it the reference to itself, equality with itself, the sublating of the restriction. The finite is therefore itself this sublating of itself; it is itself this, to be infinite.

As the concept of the infinite has thus emerged, it is the otherness of otherness, the negation of negation, the reference to itself through the sublating of determinateness. — The infinite in this its simple concept can become the second definition of the absolute; this concept is deeper than becoming; but here it is still saddled with a determinateness; and the main thing is to keep the genuine concept of infinity apart from bad infinity, reason's infinite apart from the understanding's infinite.

It first showed itself in determinate existence that existence, in its being-in-itself, determines itself as finite and goes out beyond itself as beyond the restriction. It is therefore in general the nature of the finite itself to go out beyond itself, to negate the negation and to become infinite. The infinite therefore does not stand above the finite as something finished on its own account, so that the finite would have and keep its abiding outside of it or beneath it. Nor is it we, merely as a subjective reason, who go out beyond the finite into the infinite. As when it is said that the infinite is the concept of reason, and that through reason we raise ourselves above the temporal and the finite, this happens quite without prejudice to finitude, which that elevation, remaining external to it, in no way concerns. But insofar as the finite is itself raised into infinity, it is just as little an alien force that does this to it; rather this is its nature, to refer itself to itself as to a restriction, and thus to go out beyond that restriction. For as has been shown, the restriction only is insofar as it is gone out beyond. Infinity in general therefore does not consist in the sublating of finitude in general; rather the finite is only this, to become that itself through its own nature. Infinity is its determination, or that which it is in itself.

2. Reciprocal Determination of the Finite and the Infinite

Infinity is the determination of the finite, but this determination is what is determinate itself. Infinity is therefore itself determinate, reference to an other. But the other to which the infinite refers itself is the finite. Yet they are not merely others in general over against each other; both are negations, but the one is the negation that is in itself, the other the negation as not being in itself, negation as non-being, as something sublated.

According to this its determinateness over against the infinite, the finite is negation as the determinateness on existence; it is not the negation of negation, but the first negation, or the one that has indeed sublated being within itself yet keeps it stored up within itself, merely the immediate negation. The finite therefore, as real existence, stands over against the infinite as its negation. Both stand only in reference to each other; the finite is not yet truly sublated but remains standing over against the infinite; immediately the infinite has likewise not truly sublated the finite within itself but has it outside itself.

The infinite posited in this way is the bad infinite, or the infinite of the understanding. It is not the negation of negation but is brought down to the simple first negation. It is the nothing of the finite, which is the real; it is the empty, determinationless beyond of existence. — In this way it is indeed the determination of the finite to become infinite, but the finite does not have this its determination on its own self; its being-in-itself is not in its existence but a beyond of it.

This infinite is the same empty abstraction that at the beginning stood over against being as nothing. There it was the immediate nothing; here it is the nothing that comes back and emerges out of existence, and that stands in reference to existence as merely immediate negation. Because the finite thus remains over against it as existence, the infinite has its limit on the finite and is thus only a determinate, self-finite infinite.

Thus to representation the finite appears as the actual, and the infinite by contrast as the unactual, which in a dim, unreachable distance is supposed to be the in-itself of the finite yet at the same time only its limit; for the two are outside and beyond one another.

They are outside one another, yet by their nature absolutely referred to each other; each is the limit of the other and consists only in having this limit. In their separation each therefore has at the same time this its other on its own self, but as the non-being of itself, repelling it from itself just as immediately. Their unity is thus not the reference posited on them; that reference is rather their reference as absolute others, of finitude as reality, of infinity as negation. — Their unity of concept is the determination, in which the ought and the restriction were the same, and out of which finitude and infinity have sprung. But this unity has hidden itself in the otherness of the two; it is the inward one, which merely lies at the ground; — hence the infinite seems merely to come forth on the finite, and the finite on the infinite, the one other on the other, that is to say, each seems to be a coming-to-be of its own, an immediate coming-to-be, and their reference merely an external one.

One therefore goes out beyond the finite into the infinite. This going-beyond appears as an external doing. In this void what comes to be? What is the positive in it? For the sake of the unity of the infinite and the finite, or because this infinite is itself limited, the limit comes to be; the infinite sublates itself again, its other, the finite, has entered. But this entering of the finite appears as a doing external to the infinite, and the new limit as something that does not come to be out of the infinite itself. There is thus present the relapse into the previous, sublated determination. This new limit, however, is itself only something that is to be sublated, or gone out beyond. Thus the void, the nothing, has come to be once more, in which, however, that determination, a new limit, can be posited, and so on into infinity.

There is present the reciprocal determination of the finite and the infinite; the finite is finite only in the reference to the ought or to the infinite, and the infinite is infinite only in reference to the finite. They are absolute others over against each other, and each has the other of itself on its own self.

It is this reciprocal determination which appears more precisely in the quantitative sphere as the progress into infinity, which in so many shapes and applications counts as an ultimate, beyond which one goes no further; rather, having arrived at that: And so on into infinity, thought is wont to have reached its end.

The reason why this going-beyond is not itself gone beyond has emerged. Only the bad infinite is present; one does indeed go out beyond it, for a new limit is posited, but by that very act one rather only returns to the finite. Bad infinity is the same as the perennial ought; it is indeed the negation of the finite, but it is not able to free itself from the finite in truth; the finite comes forth again on infinity itself, as its other, because this infinite only is as in reference to the finite that is other to it. The progress into infinity is therefore only the self-repeating sameness, one and the same tedious alternation of this finite and this infinite.

This infinity of the infinite progress, which remains saddled with the finite, has its other, the finite, on its own self; it is thereby bounded and itself finite; it is the bad infinity for the reason that it is not in and for itself but only is as reference to its other.

This infinite is itself finite. — It would thus in fact be the unity of the finite and the infinite. But upon this unity no reflection is made. Yet it alone is what calls forth the infinite within the finite and the finite within the infinite, and is, so to speak, the mainspring of the infinite progress. The progress is the outward side of that unity, at which representation comes to a halt, at that perennial repetition of one and the same alternating, at the empty restlessness of moving on out beyond the limit, a moving-on that finds a new limit in this infinite yet can hold itself on that limit as little as it can within the infinite. This infinite has, on the one hand, the fixed determination of a beyond, which therefore cannot be reached, and that because it is not supposed to be reached, because it has the determination of a beyond. According to this determination it has the finite over against it, as the determination of a this-side; a finite which can just as little raise itself into the infinite, and that because it has this determination of an other for it.

3. Return of Infinity into Itself

In fact, however, the truth of this infinite is already contained in this reciprocal determining that passes over and back. For it is, as was recalled, itself finite, being absolutely referred to the finite. The unity of the finite and the infinite is therefore not merely the inner, but is itself present. The infinite is only as the going-beyond of the finite; the finite likewise only as that which is a limit and beyond which one must go. In each of them, therefore, lies that determination which in the supposing of the infinite progress or of the ought is merely shut out from it and stands over against it.

But the unity of the finite and the infinite sublates them; for finite and infinite is precisely what they are only in their separation. Each, however, is on its own self this unity and this sublating of itself. Finitude is only as a going out beyond itself; contained in it, therefore, is infinity, the other of itself. Just so, infinity is only as a going out beyond the finite; it has meaning only as the negative reference to the finite, it therefore essentially contains its other, and is thus on itself the other of itself. The finite is not sublated by the infinite as by something that is outside it; rather its infinity consists in sublating itself. — Further, this sublating is not otherness in general; rather the finite, according to its determination, as what it is supposed to be in itself, is negation, is otherness, is existence as a non-being. Since it thus has the otherness of its determination on its own self, it is itself the otherness of otherness. — Thus infinity does not consist in the empty beyond, which is bounded only externally and receives a determination; rather infinity is likewise on itself the other of itself, which calls itself back out of its flight, and thus, as other of the empty otherness, as negation of negation, is return to itself and reference to itself.

Neither the finite as such nor the infinite as such therefore has truth. Each is on its own self the opposite of itself, and unity with its other. Their determinateness over against each other has therefore vanished. With this there has entered true in finity, in which both finitude and bad infinity are sublated. It consists in the going out beyond otherness, as the return to itself; it is negation as referring itself to itself; otherness insofar as it is not immediate otherness but the sublating of otherness, the restored equality with itself.

Existence is at first determinate being, essentially referred to an other. Non-being is in existence as being; and existence has now made itself into this on its own self, namely as infinity. The determinateness of existence has vanished as reference to an other; it has become determinateness referring itself to itself, absolute, restrictionless being-determined. This pure being-determined within itself, not through an other, qualitative infinity, being that is equal to itself, as the negative reference to itself, is being-for-itself.

Remark

The infinite, — in the ordinary sense of bad infinity, — and the progress into infinity, like the ought, are the expression of a contradiction that takes itself for the resolution, or for what is ultimate. This infinite is a first elevation of sensuous representing above the finite into thought, a thought that however has only the content of nothing, — a flight beyond what is limited, a flight that fails to collect itself inward and cannot carry the negative back into the positive. This incomplete reflection places negativity in the beyond, while the positive or the real stays on this side. Although the elevation of the finite into the infinite and the calling back of the beyond into this side, or the sublating of these two imperfect determinations, is present, reflection nevertheless does not bring these two thoughts together. The nature of speculative thinking consists solely in grasping the opposed moments in their unity. Since each of them shows in itself that it has its opposite on its own self, its positive truth is this unity, the taking together of both thoughts, their infinity, the reference to itself, not the immediate reference but the infinite one.

The essence of philosophy has often been placed, by those who are already more familiar with thinking, in the task of answering how the infinite comes out of itself and to finitude? — The infinite at whose concept we have arrived will determine itself further in the course of this exposition, and will thereby show on itself what is demanded, namely how it, if one wishes to express it so, comes to finitude. Here we consider this question only in its immediacy, and with regard to the sense considered just now which the infinite is wont to have.

On the answering of this question it is supposed to depend whether there is a philosophy at all, and while one gives out that one is willing to let the matter turn on this, one believes at the same time to possess in the question itself an invincible talisman by which one is made firm and secure against the answer and thereby against philosophy in general. — With other subject matters too it presupposes a formation to understand how to ask, but still more with philosophical subject matters, if one is to receive an answer other than that the question is worthless.

With such questions it is customary, in respect of the expression, to lay claim to the fairness that the words do not matter, but that in one or another manner of expression what does matter is intelligible? Expressions of sensuous representation, like going out and the like, which are readily used in the question, arouse the suspicion that the home from which the question stems is the soil of ordinary representing, and that for the answer, too, representations current in common life and the shape of a sensuous simile are expected.

If instead of the infinite being in general is taken, then the determining of being, a negation on it, seems more easily comprehensible. For being is indeed itself the indeterminate; insofar therefore as it is determined, it is the determinate indeterminate, unity of determinateness and indeterminateness. But it is not immediately expressed on being that it is the opposite of what is determinate. The infinite by contrast contains this expressed; it is the not-finite. The unity of the finite and the infinite thus seems immediately shut out; incomplete, representing reflection is therefore most stubborn against this unity.

But it has been shown, and it is immediately evident, that the infinite, and indeed in the sense in which it is taken by that reflecting, — namely as standing over against the finite, — has its other on the finite for the very reason that it stands over against the finite, and is therefore bounded and itself finite. The answer to the question how the infinite becomes finite is accordingly this, that there is no infinite which is at first infinite and which would need only afterwards to become finite, to come to finitude; rather it is already for its own self just as much finite as infinite. Or since the question assumes the infinite on the one side for itself, and assumes that the finite, which has gone out of it into separation, is, in its severance from it, genuinely real, or that if not precisely this finite then at least that infinite is the truth, — one could say that this separation is indeed incomprehensible. For neither such a finite nor such an infinite has truth; but the untrue is incomprehensible. One can therefore say that this question sets up an untrue content and contains an untrue reference of that content. It is thus not to be answered; rather the false presuppositions that it contains, or the question itself, are to be negated. But what was already noted above concerning the unity of being and nothing is to be recalled, namely that the expression: unity of the infinite and the finite, or: that finite and infinite are the same, also has a lopsided side, because it expresses as motionless being what is a becoming. Thus the infinite too is the becoming towards the finite, and conversely the finite the becoming towards the infinite. One can say in this way that the infinite goes out to the finite, and indeed for the reason that it has no truth, no subsistence on its own self; so conversely the finite goes into the infinite, on the same ground of its nullity. But the question assumes the infinite that stands over against the finite as something genuine; or else the reference-less infinite, which however ought then to be called not infinite but being; yet with being it has already shown itself that this pure immediate unity has no truth.

Chapter 3. Being-for-itself

In being-for-itself the qualitative being is completed; it is infinite being. The being of the beginning is without any determination. Existence is sublated being, but only immediately sublated being. It therefore contains at first only the first, immediate negation; being is likewise present as preserved, and determinateness is as yet only limit. The movement of existence consists in shifting this limit out of its externality and into itself. In being-for-itself this reversal is completed. The negative as being-within-itself and the negative as limit, as otherness, are posited as identical; being-for-itself is the negative that refers itself to itself, absolute being-determined.

Now just as existence determines or makes itself into the existent, so first being-for-itself determines itself into that which is for itself, or into the one.

Second, the one is repulsion and passes over into a plurality of ones.

Third, however, this otherness of the one sublates itself through attraction, and quality, which in being-for-itself drove itself to its extreme point, passes over into quantity.

A. Being-for-itself as Such

What has now resulted is the general concept of being-for-itself. Within it there fall apart the moments of its infinite reference to itself and of being-for-one. Taken as this reflected being-for-itself, it is ideality. Taken, however, as the unity of its moments, a unity that in its own self turns back into itself, it is the one.

1. Being-for-itself in General

Whatever is for itself is such by virtue of sublating otherness, and the reference to and community with an other. What is other is present in it only as a sublated one, as one of its moments. Being-for-itself does not pass out beyond itself so as to be for itself a restriction, an other; it consists rather in having already passed beyond the restriction, beyond its otherness, and in being the infinite turning back into itself precisely as this negation.

2. The Moments of Being-for-itself

Being-for-itself, as negation of otherness, is reference to itself; equality with itself. This makes

a.) the moment of its being-in-itself,

up. This being-in-itself, however, is determined further than it was in existence. The being-in-itself of existence is inert, gets determined, and does not maintain itself against the limit and against being limited; just as the being-in-itself, as determination, is indeed equal to its restriction, or becomes its own restriction, yet in such a way that in it it is simply the non-being of itself. In the being-in-itself of existence being-for-other is likewise sublated; but this sublating consists rather only in the distinguishing and separating of the two from one another, and this separating belongs to an external reflection. — Determination, or the ought, and restriction are indeed in itself one and the same determinateness, which is however posited the one time as being-in-itself over against non-being, and the other time as this non-being or as absolute otherness; they are the same only in itself, and this because they have not yet, in their very differentiatedness, sublated themselves in their own selves and are not yet the same for itself.

The being-in-itself of being-for-itself, by contrast, has the determination of this sublating; being-for-itself is thereby, even in the differentiation, in existence, the unity which the ought and the restriction, or the infinite progress, only is in itself. It is existence closed within itself, infinite reference to itself. Insofar as it is reference to an other, it is reference to it only as to something sublated; in the other, therefore, it is reference only to itself.

b.) Being for One

The infinite reference of being-for-itself to itself consists in the equality of the negation with itself. Otherness, however, has not vanished, as though being-for-itself were only the immediate reference of being to itself; rather it is something sublated. Otherness is not distributed between being-for-itself and an other; being-for-itself does not have non-being on it as limit or determinateness, and therefore not as an existence other than itself either. The other is therefore no existence at all, no something; it is only within being-for-itself, is nothing apart from the latter's infinite reference to itself, and thus has only this existence, to be for one.

This second moment of being-for-itself expresses how the finite is in its unity with the infinite. Being-for-other in existence, or existence in general, likewise has this side of being for one; but besides that it is also in itself, indifferent towards this its limit.

Remark

The expression our language has for the question about quality, an expression that at first appears peculiar, what kind of thing something may be, chiefly brings out the moment considered here. Determinateness is voiced in it not as something that is in itself, but as something that only is for one. This idealistic expression does not, in so asking, inquire what thing A may be for another thing B, nor what this human being may be for some other one; — but rather, what kind of thing, what kind of human being, this is? in such a way that the being-for-one is at once withdrawn into the thing, into the human being himself, or that the one which is, and the one for which it is, come to a single selfsame thing, — an identity that is now to be considered in the case of ideality.

c.) Ideality

Being-for-itself is simple equality with itself. It has the two distinguished moments within it because simple equality with itself is not the immediate, being, but only is as sublating of otherness; it therefore contains at the same time a separation, or otherness, yet as a vanishing separation, as self-sublating otherness. The two moments are therefore inseparable. The infinite reference to itself is only as negation of the negation, and this sublating of otherness is immediately a unity referring itself to itself.

Being-for-itself in this determination, that it refers itself to itself in that the other is in it only as something sublated, is ideality.

Ideality is therefore the same as what infinity is, or it is the positive and reflected, determinate expression of infinity. What is infinite is ideal; it is without restriction only insofar as the other only is for it. If the other had an existence, then it would not be merely a for-one, but would constitute a limit.

Ideality and reality are one and the same — that is one of the skewed expressions already censured. Ideality is rather the truth of reality, or, if by reality one wishes to understand the substantial, the true itself, then ideality is the genuine reality; namely insofar as existence or reality has determined itself into ideality.

Just as reality seemed to have distinguished meanings according to its two sides, that of being-in-itself and that of being-for-other, so too the ideal seems to be distinguished in the sense of being-in-itself, as infinite reference to itself, and in the sense of being-for-other, namely as being-for-one.

— Thus spirit, God, the absolute in general, is something ideal, as infinite reference to itself, as unity with itself which is not lost in externality and in otherness, but for which all determinateness is. — The Leibnizian representing essence, the monad, is essentially something ideal. Representing is a being-for-itself in which the determinatenesses are not limits but only moments. Representing is admittedly a more concrete determination, one belonging to consciousness, but here it has no further meaning than that of ideality; for even what is wholly without consciousness is something representing. In this system, then, otherness is sublated altogether; spirit and body, or the monads in general, are not others to one another, they set no limit to each other, they exert no influence upon each other; every relation whatever having an otherness for its ground drops away. That there are several monads, and that they are thereby determined as others as well, is no concern of the monads themselves; it is the reflection of a third party falling outside them; they are not others in their own selves. — Yet precisely here lies at the same time what is unfinished about this system. Only in themselves, or in God, the monad of monads, or else in the system, are the monads something representing. But otherness is likewise at hand; let it fall where it will, into representation itself, or however that third be determined which regards them as others. The other is therefore not sublated in its own self; it is only excluded, and the monads are posited as such that are not others only through abstraction. Or if it is a third that posits their otherness, then it is also a third that sublates their otherness; but this entire movement, which makes them into something ideal, falls outside them.

Other idealism, for instance the Kantian and Fichte's, does not get beyond the ought or the infinite progress, and with this does not attain idealism and being-for-itself. In these systems the thing-in-itself, or the infinite check, does indeed step immediately into the I and becomes a mere for-it; but it starts out from a free otherness. The I is therefore indeed determined as the ideal from the side of being-in-itself, as infinite reference to itself; but the side of being-for-one is not completed, and therefore neither is that first side.

The ideal is secondly also being-for-one. This sense is distinguished from the first, the infinite reference to itself. In the former sense God, the I and so forth are called something ideal, and being-for-itself proper, infinity, is restricted to that sense, so that God, the I would in this way be only something ideal in that they simply would not be for-one. — In this other sense an empty theory is called something merely ideal. The ideal then has roughly the meaning of a mere fancy, at least of a mere representation to which nothing actual corresponds, whose content is nothing for itself.

Insofar, however, as this difference is held fast, existence and a something have remained over for representation, or have returned precisely through that very determining. As if, namely, a something were at hand which subsisted as ground or subject, and for which the other is, just as there were a something which would be only what is referred; the former the something that is for itself, the latter only the something that is for other. But being-for-one and being-for-itself do not constitute genuine determinatenesses over against one another. Being-for-one expresses the sublatedness of otherness; it is therefore essentially one with being-for-itself. Being-for-itself is infinite reference to itself in that it is sublated otherness. Insofar as the difference is assumed for a moment, and something that is for itself is already spoken of here, then what is for itself is itself that to which it refers as to the sublated other, which is accordingly for-one. Being-for-itself is reference to itself, but infinite reference; negation is therefore contained in it. Or what is for itself is not something immediate, not something that is; but this non-being is simply sublated; it is therefore itself the sublated other, being-for-one; through this it refers, in its other, only to itself. The ideal is therefore necessarily for-one, but it is not for an other; or the one for which it is, is only itself.

The I, then, spirit in general, or God, are ideal because they are infinite; but they are not ideal as beings-for-themselves distinguished from that which is for-one. For in that case they would be only immediate ones, or more precisely they would be existence, a being-for-other, since what would be for them would not be themselves but an other, if the moment of being for-one were not to belong to them. God is therefore for himself insofar as he himself is that which is for him.

Being-for-itself and being-for-one, then, do not signify different meanings of ideality; they are its essential and inseparable moments.

3. Becoming of the One

Being-for-itself is ideality; and it is, as has just now emerged, the simple unity of its moments, and properly no difference of them at all. It contains otherness as sublated; the sublating of otherness and the reference to itself are the same; there is only one determination at hand, the reference-to-itself of the sublating. The inner moments of being-for-itself have therefore in fact collapsed into differencelessness.

Being-for-itself is therefore a simple being-one with itself, a being-within-itself that has no limit or determinateness, or whose determinateness is pure negating. Since it is on the whole the self-referring sublating, this simple equality with itself, it is thus a being-within-itself which has the form of immediacy; a something, but an undeterminable one.

In accordance with this immediacy, this being-within-itself is not a referring but a being. But as immediacy grounded upon negating, it is at the same time essentially reference, and this constitutes its determination. Its immediacy and this its determination are therefore distinguished from one another. With its simple immediacy, or as being, it is at the same time pure negating, a reference outwards in general, a purely negating referring; but not to an other; for here there is no other at hand any more, but rather one simply sublated. This reference is also not yet a reference to the immediate; rather, this immediacy is at first nothing other than the simple referring of the negation to itself.

What is posited, then, is the return of ideality into simple being-within-itself, into a self-equality which has the form of immediacy and which is a merely negative referring, a referring to nothing at all. Being-for-itself, as this immediate which is pure negating, is that which is for itself, the one.

B. The One

1. The One and the Void

The one is the simple reference of being-for-itself to itself which, since its moments have collapsed into one another, has the form of immediacy. It therefore simply is, without having an existence; determinate being or existence has, in being-for-itself, returned to pure being.

Because the one has no existence and no determinateness as reference to an other, it is also capable of no constitution and hence of no otherness; it is unalterable.

It is indeterminate, but not in the way being is; rather its indeterminateness is the determinateness which is reference to itself, absolute being-determined. — Absolute being-determined is determinateness, or negation, as reference not to an other but to itself. This equality of the one with itself it has, then, only insofar as it is negating, a direction away from itself, out towards an other, a direction that is however immediately sublated, turned back, because there is no other for it to go to, and that has returned into itself.

Because, for the sake of the simplicity of this being-returned-into-itself, the one has the shape of something immediate, of something that is, its sublating, or the negation, appears as an other that is outside it, an other which is not a something but the nothing, which itself has the shape of immediacy over against that which is, yet which in itself is at the same time not the first nothing, is not immediate, but the nothing as sublated something — or it is the nothing as the void.

The void is therefore in truth not immediate, not indifferent on its own account over against the one; rather it is the one's referring-itself-to-an-other, or its limit. But the one itself, as absolute being-determined, is the pure limit, the pure negation or void. In comporting itself towards the void, therefore, it is the infinite reference to itself. It is itself, however, the pure negation as immediately equal to itself, as something that is; the void, by contrast, is the same negation as non-being.

Being-for-itself, having in this way determined itself as the one and the void, has again attained an existence. But just as something and an other have, so to speak, being for their soil, upon which their determinateness is posited, so the one and the void have the nothing for their common, or rather simple, soil. Being-for-itself has the difference at first within its own self, and the differentiated terms as its moments, being-for-itself as being-in-itself, and being-for-one, whose unity is ideality. They step out of this unity, or become the mutually external terms, the one and the void, in that through the simple unity of the moments themselves the determination of being comes in, whereby what was previously a moment receives the shape of something that is. — Or there are two moments, simple being-for-itself and being-for-one; each considered on its own, and each also is on its own in this way, for each is also the whole, collapses in the simple reference to itself into immediacy, and with this into existence over against the other, into a reference between such terms as are not only referred but also immediate.

Remark

The one in this form of existence is that stage of the category which appeared among the ancients as the atomistic principle, the principle that what things are in essence is atoms and the void, (το ἀτομον or τα ἀτομα και τοκενον.) Abstraction, ripened to this form, has won a determinateness greater than Parmenides' being and Heraclitus' becoming. High as it stands in raising this simple determinateness of the one and of the void to the principle of all things, in tracing the world's infinite manifoldness back to this simple opposition, and in making bold to cognize that manifoldness out of it, just as easy is it for representational reflecting to picture atoms here and the void alongside them. No wonder, then, that the atomistic principle has held its ground at all times; the relation of composition, just as trivial and external, which has still to be added in order to arrive at the shine of a diversity and manifoldness, is quite as popular as the atoms and the void themselves. The one and the void is being-for-itself, the highest being-within-itself sunk down into complete externality; for in the one there is present the immediacy or the being which, since it negates all otherness, is no longer determinable and alterable, and therefore seems also to be unable to turn back into itself again, but for which, in its absolute brittleness, all determination, manifoldness, connection remains a simply external reference.

With the first thinkers of the atomistic principle, however, it did not remain in this externality; besides its abstraction it also had the speculative depth that the void was cognized as the source of motion; which is a quite other reference of the atoms and the void than the mere side-by-side and the indifference of these two determinations towards one another. That the void is the source of motion does not, however, have the trifling sense that something can move only into a void and not into an already filled space; in which understanding the void would be merely the presupposition or condition, not the ground of motion, just as motion itself would be presupposed as at hand and the essential thing, the thought of a ground of it, forgotten. The view, by contrast, that the void constitutes the ground of motion contains the profound thought that in the negative as such there lies the ground of becoming, of that unrest which is self-movement. Here, however, the negative is to be taken not as the nothing that lies closest to representation, but as genuine negativity, as the infinite.

2. Many Ones

(Repulsion.)

The one and the void constitute being-for-itself in its existence.

Each of these moments is at the same time the negation; the one and the void therefore constitute the reference of negation to negation. But the determinateness of this existence, as it has emerged, is that the one is the negation in the determination of being, whereas the void is the negation in the determination of non-being. This as yet abstract difference has to determine itself further.

The one has immediacy; it is reference to itself and, on its own account, indifferent towards the nothing that is outside it. But the one is essentially not indifferent towards the void; for it is reference to itself only as referring negation, that is, as that which the void outside it is supposed to be. Insofar, therefore, as first the one as something immediate refers itself to the void, which likewise has the shape of something immediate, the reference of existence is at hand; the one thus refers itself to the void as to an other of itself, and goes out beyond itself into the void. But since second in the ideality of being-for-itself there is no other, since the reference to its non-being is essentially reference to itself, the existent other is at the same time itself, and at the same time its non-being. The one is thus a becoming into many ones.

This movement of the one into many ones is, however, not so much a becoming; for becoming is a passing over into the opposite, from being into nothing, and it is a reference which is not immediately the referred term itself. Here, by contrast, one becomes only one; further, the one, the referred term, is this negative reference itself.

For the one is reference to itself as negative referring; thus it is being-for-itself in general, a referring without anything referred. But insofar as it is one, it is immediate; and it is therewith essentially reference to itself as to something immediate; there is therewith a referred term at hand, but through absolutely negative reference, which is infinite sublating of otherness. The one therefore does not pass over into an other; rather, it repels itself from itself. The negative reference of the one to itself is repulsion.

Repulsion is therefore indeed a becoming of the many ones, but through the one itself.

For that reason the one is also not as something that has become; the becoming into many vanishes immediately as becoming; those that have become are ones, are not for an other, but refer themselves infinitely to themselves. The one repels only itself from its own self; it therefore does not become, but already is; this becoming is accordingly no passing over.

Plurality is thus not an otherness, and is a determination wholly external to the one. The one, in repelling its own self, remains reference to itself, does not become a referring to an other. That the ones are others over against one another, that they are gathered together into the determinateness of plurality, is therefore no concern of the ones. Were plurality a reference of the ones to each other, they would set limits to each other or would have a being-for-other. Their reference, insofar as they are represented as immediate, is the void, or no reference at all. The limit is that wherein what is limited just as much is as is not; the void, however, has the determination of pure non-being, and only this makes up their limit.

The repulsion of the one from its own self is therefore infinity come outside itself; it is just as much a simple referring of one to one as rather the absolute referencelessn[e]ss of the ones. Or the plurality of the one is the one's own positing; the one is only the negative reference of the one to its own self, and this reference — that is, the one itself — is the many ones. But just as much is plurality no concern of the one, it is simply external to it; for the one is just this sublating of otherness, repulsion is the one's reference to itself, and simple equality with itself.

Remark

Leibniz's idealism was spoken of a short while ago. It may be added here that this idealism, starting from the representing monad, from being-for-itself, got no further in the further determination of this being-for-itself than the repulsion just now considered, and indeed no further than plurality, in which each of the ones is only for itself, indifferent towards the existence and the being-for-itself of others, or in which others are not there for the one at all. For itself the monad is the whole self-enclosed world; not one of them stands in need of the rest. The inner manifoldness that it has in its representing is of no concern to us here; for it changes nothing in its determination of being for itself; the monad, since the manifoldness is an ideal one, remains referred to itself alone, the alterations unfold within it and are no references of the monads to one another; what, according to the real determination, is taken as a reference of the monads to one another is an independent and merely simultaneous becoming. Leibniz's idealism, moreover, picks up plurality immediately as something giv en, and does not comprehend it as a repulsion of the monad. Hence it has plurality only from the side of its absolute externality, not from the side on which the monad's reference to itself, being negative, is just as much itself plurality; — the two moments that repulsion holds together within itself. Atomism, for its part, is without the concept of ideality; the one it fails to grasp as a something having within its own self both moments, that of being-for-itself and that of being-for-it; hence not as something ideal, but only as something simply and immediately for itself. Against that, it does pass beyond the merely indifferent plurality; the atoms do after all enter into a further determination over against one another, even if not through repulsion itself; whereas in that indifferent independence of the monads plurality, which is their fundamental determination, as was already recalled above, falls, if anywhere, only within the monad of monads or within the philosopher who observes them, and is not a determination of the monads in themselves. Or precisely insofar as plurality is not a determination of the monads in themselves, insofar as they are not others for one another, this determination belongs to appearance alone, is external to their essence, and their truth is only the substance which is One.

3. Mutual Repulsion

1. Repulsion makes up the reference of the one to itself, but is just as much its coming-outside-itself. This coming-outside-itself, the plurality of the ones, is the repulsion of the one from itself; hence not a determination external to the one, not distinct from repulsion as simple reference to itself. Considered more closely, the one refers to itself as to something immediate; but immediacy is being; repulsion, however, as the negation that refers itself to itself, is not immediacy or being. The one therefore refers to itself at the same time as to its absolute non-being; it is a repelling of itself away from itself; what has been repelled is on the one side indeed the one itself, but just as much its non-being. This repelled thing, itself as one, is something immediate, and at the same time is determined as the non-being of what refers itself to itself; or as an absolutely other. Plurality at first contained no otherness; the limit was only the void, or only that wherein the ones are not. But they are in the limit as well; they are within the void, or their repulsion is their common reference.

The repulsion of the one, then, in being a repelling of itself away from itself, is at the same time a repelling of the one as of an other away from itself, and with that a mutual repelling of the many ones.

The many in this way stand, as repelling one another, in reference to one another; they preserve themselves in repulsion as beings for themselves; their reference consists in negating their reference.

This mutual repulsion is what first makes up the existence of the many ones; for it is not their being-for-itself, which would be differentiated only within a third, but their own self-preserving differentiating. More closely determined, insofar as therein each preserves itself against the others, it is a mutual excluding. Or this reference is a merely relative repulsion. They negate one another, that is, they posit one another as such as are only for-one. But they negate at the same time, and just as much, this, to be only for-one; they repel this ideality of theirs.

2. In this existence of the many ones there thus come apart the moments that in ideality are united without qualification. In its being-for-itself the one is indeed also for-one, so much so that this sublatedness of otherness is its reference to itself. But at the same time being-for-one, as it stands determined in relative repulsion, in excluding, is a being-for-other. Each is repelled by the other, sublated, and made into something that is not for itself but for-one. Its being-for-one accordingly falls not only within the one as such itself, but within another one as well, and is being-for-other.

The being-for-itself of the many ones is hereby their repulsion against one another, whereby they so preserve themselves that they mutually sublate one another and posit the others as a mere being-for-other. But at the same time repulsion consists in repelling this ideality, and in positing itself as not being for-an-other. Yet the two are once more one and the same reference; mutual repulsion is mutual sublating, each preserves itself only in positing the others as a being-for-other, as a non-existence, and just as much only in sublating this, being for an other.

3. Being-for-other is to that extent as much sublated as it is present. But it is posited and sublated in different respects. The ones are immediate; they refer themselves to one another repellingly, sublatingly; they thus mutually bring the being-for-itself of the others down to being-for-other; this moment therefore has its place in reference to others. But the one sublates this its being-for-other; this moment is its reference to itself. The one is being-for-other only within others; but this sublatedness of the one is no concern of the one; within it the others are not as existent, immediate others, but only as sublated, and through this it refers itself to itself.

The one was repulsion in that it repels itself away from itself, and since what is repelled is accordingly only the one itself, it is thereby immediate return into itself. But this repelling has passed over into the repulsion of others and of being-for-other away from itself. The one preserves itself for itself only by referring itself negatively to others, and, this negation being mutual, by sublating the being-for-one that it therein receives. Repulsion, the repelling of the one away from itself, has thus passed over into a repelling of the others, into the positing of the others as being only for-one, and with that into the sublating of its being-for-other, into attraction.