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.

C. Attraction

Repulsion is the self-splintering of the one, at first into many, and then, for the sake of their immediacy, into others. But since the ones are simply many and equally others, no difference among them is thereby present, and the absolute being-determined of the one on its own self is not yet realized. For the one as the ideal, which is just as much for itself as it is for one, both in a single identity, collapses, for the sake of this lack of difference, into the immediacy of being. Because in this ideality no genuine other is present, no genuine sublating of otherness takes place either, and hence no real ideality. The latter now comes to be in attraction. Repulsion does indeed contain others; but since the many ones are one and all others to themselves, their repulsion holds itself in equilibrium; they themselves sublate their mutual being-for-one. They repel repulsion, or otherness.

Now in that the one ceases to be the merely simple reference of negation to itself, and arrives at a determinate difference within itself, it becomes totality, or the identity of ideality and reality. The absolute being-determined has then reached its summit, it has gone back into itself; and quality, the immediate being-determined through an other, or otherness as such, becomes something indifferent; at this unity compact within itself, quality becomes quantity.

1. One One

Repulsion makes the many ones into beings-for-other. But it is the many to which this repelling accrues, and it accrues to them as ones. Yet as ones they are infinite reference to themselves, and as such they just as much repel this being-for-other, or that repelling. This repulsion of repulsion is thus, as self-sublating, attraction.

Here, however, the difference mentioned enters in; the one, namely, posits the other ones as being-for-other, and — insofar as this repelling were mutual — sublates its being-for-other, which it would therein receive; the being-for-other of the others, however, it preserves.

Attraction, namely, is repulsion of repulsion. The one posits the other ones ideally, as being-for-other, but just as much sublates this being-for-other again. Thereby the return of the one into itself is posited, or that same infinite reference to itself which the one in itself is. But with this there are two sorts of one present; namely the immediate one, or the one as it is in itself, and then the one that out of its dispersion, out of plurality, returns into itself.

This one may be called the real one insofar as it returns into itself out of plurality and out of being-for-other, and has this moment upon it, though as a sublated one; or insofar as the moment of being-for-one which it contains in its ideality is no longer merely this abstract moment, but the immediate ones make it up. The other one, by contrast, is this immediate one that does not return into itself, that essentially is as something sublated, and remains in being-for-other.

That first one is the attracting one; the one that gives itself its moment of being-for-one at the immediate ones. These become attracted. They are immediate; but the one is essentially this, not to be an immediate being; for it is rather the negation that refers itself to itself. Since, then, they are immediate, they are only unequal to themselves, others on their own selves.

With this there is also present the otherness that is in itself, and the earlier, merely external otherness has vanished. The immediate one is only as something sublated, which is only for-other. But the being-for-itself which is only for-other is precisely otherness on its own self.

Further, the attracting one, which sublates being-for-other within itself and returns out of it into itself, is precisely thereby no longer the simple being-for-itself, but that which has otherness too as a moment within its own self.

The attracting one, then, as returning into itself out of plurality, determines itself as one, it is one as not being many, one One.

2. Equilibrium of Attraction and Repulsion

Being-for-itself, which has determined itself as one, first loses itself as plurality in absolute externality, and preserves itself therein not so much according to its immediacy, — insofar as the many are also ones, — as it restores itself out of it into one One.

This one that has returned into itself is not merely the simple reference to itself, but the reference to itself as to sublated otherness. — Further, otherness as it occurs here is not the immediate otherness of existence as such, but the one's own otherness, plurality. Being-for-itself, according to its having become out of existence, is indeed already in itself sublated otherness; but here it had once more to posit its other upon its own self, in order to be also in being-for-itself as such what it in itself is. Otherness, however, has within it a form other than in existence. Because being-for-itself is infinite reference to itself, otherness upon it is only plurality, itself as other.

But in that being-for-itself has thus sublated its immediacy and is being-for-itself that is for itself, being-determined has indeed within it made itself into absolute being-determined upon its own self, into the absolutely qualitative; but in this reality it has already gone out beyond quality. The one is only one One insofar as within it plurality, that is, the one itself, is sublated. — Or the one has, as one One, gone together with itself; instead of being exclusive, therefore, it has posited itself in continuity.

Attraction, namely, or the one One considered more closely: it is determined on its own self, for it is not one among the many, it has sublated plurality with in itself; it is therefore not something determinate over against an other, but has the other, and the reference to it, upon its own self. As one One, however, its absolute determinateness has likewise gone back into immediacy, and refers itself as exclusive to the many, as over against others, as over against its non-being, which would itself be immediate. But it is only one One; the many are not at all, they have sublated themselves; thus they are posited into one with the one, and the latter is no longer one as such.

The one One is in itself attraction, sublated repulsion; but this one itself begins by being something immediate; it is a one, and its reflection into itself consists precisely in sublating immediacy. The repulsion of repulsion sublates only its own being-for-other, but preserves the being-for-other of the others; yet an own being of that sort, one that would distinguish itself from others, presupposes an original, an immediate differentiatedness of the ones, which is not present. Repulsion is therefore a being-for-one of the many as such, and insofar as it is repulsion of repulsion, it is just as much a preserving of the many ones whose being-for-one is repelled by themselves. All are therefore equally attracting, all posit one another in the same manner as being-for-other, and repel the same, sublate it in their infinite reference within themselves. The many ones are thus preserved.

— Already in the sensuous representation of spatial attraction the stream of points coming to be attracted continues on; in place of the atoms that vanish in the one attracting point, another multitude steps forth out of the nothing. This becoming does not go back into the result of the one One in such a way that only the one One and nothing else would be; in that manner only the initial determination, the one and the void, would be posited, and the reality of the one, the returning into itself out of the many, would have vanished. Rather, in that it becomes itself as one One through this return, it is exclusive, one One over against many, and it thereby preserves them just as much. But the preservation of the many means nothing else than that they are attracting, that they sublate their being-for-other.

Attraction and repulsion are in this way not merely in equilibrium; they are in fact identical and indistinguishably the same. Repulsion appears at first as the excluding of the others; but this excluding is a positing of them as beings-for-other. Attraction, however, is the same, for it consists precisely in the self-preservation of the one against the others, in the sublating of them, in the positing of them as beings-for-other. Repulsion, conversely, is further the sublating of this being-for-other, through it the one preserves itself in sublating its being-negated; but attraction is precisely this sublating of its being-for-other, which sublating preserved it. Sensuous representation alone keeps up the difference between attraction and repulsion, in that it holds fast to one immediate point and lets the immediacy of the others vanish, though in fact just as much come to be again.

As repulsion repels itself, so attraction attracts itself, or is attraction of attraction. For according to its determination it is the positing of the many ones as ideal, and thereby the becoming of one One, which is to remain for itself and to sublate its being-for-other . But among the many ones that are to be sublated, all ones are comprised; attraction sublates just as much the one one whose becoming it is supposed to be. Or conversely, in that as the becoming of the one One it sublates the being-for-other of the one, it just as much sublates the positing whereby the ones come to be being-for-other, which is to say, once again, that it sublates itself.

This identity of repulsion and attraction accordingly has the result that the infinite reference of the one to itself is its being-for-other; its being-for-itself is infinite negation of itself, infinite being-outside-itself, and this being-outside-itself is conversely infinite having-returned into itself.

In itself the one is only this infinite reference to itself, whose result is the identity of attraction and repulsion; — the one is nothing apart from repulsion and attraction. But insofar as the one has received the shape of immediacy, these appear as references of the one, so that outside them it would preserve itself for itself; as if its being-for-an-other were distinguished from its being-for-itself, or rather from its being-in-itself, its infinite reference to itself. Taken, however, as in itself, distinguished from its negative reference, the one is the immediate one, the many. But just as immediately the many collapses into one, or the many is the negation of itself. For of the many each is one, or each is a many, or each distinguishes itself without qualification from the others and shuts them out from itself. Yet precisely in this they are equal to one another; each has entirely and utterly the same determinations that the other has; in this, that the one of the many is not what the other is, they are the same.

The formerly relative repulsion and attraction, which was only a reference of the ones, from which their immediacy, as reference to itself, was distinguished, is therefore in fact absolute repulsion and attraction; repulsion and attraction which are identical. What is present is that the one, as referring itself infinitely to itself, refers itself to its absolute otherness, and in referring itself to this its non-being, refers itself precisely therein to itself, and that the one is itself only this referring. Its immediacy, its being, is rather its otherness, and this its being-outside-itself is its being.

Remark

Attraction and repulsion are, as is well known, customarily viewed as forces. On this representation they are taken to be self-subsistent, so that they do not refer to one another by their nature, that is, so that neither is meant to be merely a moment passing over into its opposite, but is instead to persist firmly over against the other. They are further represented as coming together in a third, in matter; yet in such a way that this becoming-one does not count as their truth, each of them being rather something first and in and for itself, while matter is what they posit and bring forth. If it is said that matter has these forces within itself, then by this unity of theirs a linkage is understood in which the two are at the same time presupposed as free of one another, each being in itself.

Kant, as is well known, has constructed matter out of the repulsive and attractive force, or at least has laid down, as he expresses it, the metaphysical elements belonging to this construction. — To throw a closer light on this construction will not be without interest. This metaphysical presentation of an object which seemed to belong, not only itself but in its determinations, to experience alone, is on the one part remarkable because it has at least given the impetus to the newer philosophy of nature, — the philosophy which does not make nature, as something sensuously given to perception, the ground of science, but cognizes nature's determinations out of the absolute concept; on the other part, too, because people still frequently stop at that Kantian construction and take it for a philosophical beginning and foundation of physics.

A concrete existence such as sensuous matter does not, to be sure, yet belong here, any more than space and the determinations of space do. But at the base of attractive and repulsive force too, insofar as they are regarded as forces of sensuous matter, there lie the pure determinations of the one and the many considered here, together with their references to one another, which I have likewise called repulsion and attraction.

The way in which Kant deduces matter out of these forces, and to which he gives the name of a construction, does not, looked at more closely, deserve that name, unless indeed every kind of reflection, even the analysing kind, is called a construction, as later philosophers of nature have of course called the shallowest ratiocination and the most groundless brew of an arbitrary imagination and a thoughtless reflection, — a brew which helped itself especially to the so-called factors of attractive force and repulsive force and paraded them everywhere, — a constructing.

Kant's procedure is at bottom analytic, not constructive. He presupposes the representation of matter, and then asks what forces belong to it if its presupposed determinations are to be preserved. On the one part, accordingly, he calls for attractive force on this ground, because through repulsion alone, without attraction, there could properly be no matter. (Foundations of Natural Science, p. 53 f.) Repulsion, on the other part, he likewise derives from matter, and states as its ground that we represent matter to ourselves as impenetrable, since matter presents itself under this determination to the sense of feeling, through which it is said to reveal itself to us. Repulsion is thus thought immediately within the concept of matter, because it is thereby immediately given; attraction, by contrast, is attached to that concept through inferences. But at the base of these inferences lies what has just been said, namely that a matter which had merely repulsive force would not exhaust what we represent to ourselves under matter.

This, as is evident, is the procedure of the ordinary cognition that reflects upon experience, which first perceives determinations in the appearance, then lays these at the base, and for the so-called explaining of them assumes basic materials and also forces which are supposed to bring forth those determinations of the appearance.

With regard to the difference adduced, as to how repulsive force and how attractive force come to be found in matter by cognition, Kant remarks still further that attractive force, with respect to the concept of matter, does indeed belong to it just as much, although it is not contained therein. Kant singles out this last expression. It is not to be seen, however, what difference is supposed to lie in this; for a determination which belongs to the concept of a matter must truly be contained therein. —

What creates the difficulty, and brings on this empty evasion, consists in this, that Kant reckons into the concept of matter merely the determination of impenetrability, one that we are said to perceive through feeling, on account of which repulsive force, as the warding off of an other from oneself, is said to be immediately given. But if matter is not supposed to be able to exist without attractive force, then a representation of matter drawn from perception lies at the base of this; the determination of attraction must accordingly in fact likewise be drawn from perception and therefore be encounterable in it. It can indeed be well perceived that matter, besides its being-for-itself, which sublates being-for-other, also has a reference of what is for itself to one another, spatial extension and cohesion. Out of this perception reflection can derive attractive force just as immediately, or assume it as given, as it did with repulsive force. In fact, if the inferences from which attractive force is supposed to be derived are examined, (see the proof of the proposition: that a force of attraction as second fundamental force is demanded by the possibility of matter, loc. cit.) they contain nothing but this, that through mere repulsion matter would not be spatial. Inasmuch as matter is presupposed as space-filling, continuity is thereby ascribed to it, and the force of attraction is assumed as the ground of that continuity.

Even if this so-called construction of matter had at most an analytic merit, one still curtailed by the impure exposition, the basic thought remains always well worth valuing, that of cognizing matter out of these two opposed determinations as its fundamental forces. Kant is concerned above all to banish the ordinary mechanical way of representing, which stops at the one determination, impenetrability, at punctiformity that is for itself, and turns the opposed determination, the reference of matter within itself or of several matters, regarded again as particular ones, to one another, into something external; — the way of representing which, as Kant says, will otherwise allow no moving forces except through pressure and impact, hence only through action from outside. This externality of cognition always presupposes motion as already at hand, and never thinks of grasping it as something inward and comprehending it itself and within matter, but assumes matter for its part as motionless and as inert. Now although Kant does sublate this externality insofar as he makes attraction, the reference of matters to one another insofar as these are assumed to be different, or of matter in general in its being-outside-itself, into a force of matter itself, on the other side his two fundamental forces nevertheless remain, within matter, external and self-subsistent over against one another.

As null as was the difference of these two forces which was attributed to them with regard to cognition, just as null must every other difference show itself to be that is drawn in respect of their content-determination, since they, as they were considered above in their truth, are only moments which vanish into one another. I take up these further determinations of difference as Kant states them.

He determines attractive force as a penetrating force, repulsive force as a surface force. The ground adduced for the latter's being only a surface force is the following: „The parts touching one another bound each the space of action of the other, and repulsive force cannot move a more distant part except by means of those lying in between; an immediate action of one matter upon another passing crosswise through these, by way of expansive forces (which here means repulsive forces), is impossible.“

I will not dwell on the point that, once nearer or more distant parts of matter are assumed, with regard to attraction there would likewise arise the difference that one atom would indeed act upon another, but that a third, more distant one, such that the other lay between it and the first attracting atom, would step first of all into the attracting sphere of the intervening atom that is nearer to it, so that the first would not exercise an immediate simple action; from which a mediated action could be developed for attractive force just as much as for repulsive force; — further, that the true penetrating of attractive force would in general have to consist solely in this, that all parts of matter were attracting in and for themselves, and not that a certain multitude behaved passively and only One atom actively. But I note immediately, with regard to repulsive force, that in the passage cited there occur parts touching one another, hence a compactness and continuity of a finished matter which does not permit a repelling through itself; this compactness of matter, however, in which parts touch one another and are no longer separated by the void, already presupposes the sublatedness of repulsive force. Parts touching one another are, according to the sensuous representation of repulsion that prevails here, to be taken as parts which do not repel one another. It follows, then, quite tautologically, that where the non-being of repulsion is assumed, no repulsion can take place. From this, however, nothing further follows for a determination of repulsive force.

In the same way it is natural to sensuous representation, presupposing as it does one attracting point and others which do not attract but are only attracted, to assume that the former brings something about with its attracting, and lays a thickness about itself as a sphere, so that within this sphere, because it stands under the dominion of that point's attraction, repulsion is sublated and can therefore take place only outside, against the surface of this sphere. — On the one part the surface appears as that which still stands in relation to an other not referred to it. On the other part, however, repulsion is itself within that sphere of attraction. Those atoms, that is, or material parts which are there for representation as attracted, are for it in fact just as much repelled ones as well (-- since we let repulsion count as removal, attraction as approach, to a determinate point —). For the attracted ones, if they were only this, would have vanished into the point of attraction, and there would be only this atom, not an attracted one distinguished from it, and hence not parts touching one another, that is, parts at the same time held apart. But insofar as such parts are assumed, repulsion is in fact not excluded from that sphere of attraction, but is present within it.

Kant adopts, further, the additional determination that by the force of attraction matter only occupies a space, without filling it. „Because matter does not fill space by the force of attraction, this force can act through empty space, since no matter lying in between sets bounds to it.“ — This difference is constituted about like the earlier one, where a determination was to pertain to the concept of a matter and yet not be contained in it. By the force of attraction matter is not to fill space, but is, in respect of this force, to relate itself to itself through empty space; — it is thus not to be seen how it is supposed to occupy space if space is empty. But further it is repulsion, if we hold to its first determination, through which the ones thrust one another away and only negatively, which here means, through empty space, refer to one another. Here, however, attractive force keeps space empty for itself, it fills space through its reference of the atoms in no way, which is to say, it keeps the atoms in a negative reference to one another. — We see accordingly that here Kant unconsciously runs up against what lies in the nature of the matter, in the nullity of the difference between repulsion and attraction, in that he ascribes to attractive force precisely what, according to the first determination, he ascribed to the opposed force. In the course of the business of fixing the difference of the two forces, it had come about that the one had passed over into the other. — Through repulsion, by contrast, matter is supposed to fill a space, so that through repulsion the empty space which attractive force leaves disappears. In fact, therefore, in sublating empty space it sublates the negative reference of the atoms or ones, that is, their repulsion; or repulsion is posited as the opposite of itself.

To this blurring of the differences just exhibited there is added the further confusion that, as was noted at the very outset, this exposition of the opposed forces is analytic, and that throughout the whole presentation matter, which is first supposed to be derived from its elements, already turns up as finished and constituted. In the definition of surface force and penetrating force both are assumed as moving forces by which matters are to be able to act in the one way or the other. — They are therefore exhibited here as forces not by which matter first comes about, but by which it, already finished, is merely set in motion. But insofar as the talk is of forces by which different matters act upon one another and set each other in motion, this is something quite other than the determination and reference which they were supposed to have as the moments of matter.

The same opposition, as attractive and repulsive force, is constituted in a further determination by centripetal and centrifugal force. These seem to afford an essential difference, since within their sphere One one, a centre, stands fast, over against which the other ones comport themselves as not being for themselves. Insofar as they are put to use for explanation, however — for which purpose they are assumed, as repulsive and attractive force are elsewhere, in an opposed quantitative ratio, so that the one waxes as the other wanes — the appearance and its inequality are supposed to result only out of them. One need only take up the first available exposition of an appearance, for instance of the unequal velocity which a planet has in its orbit around its central body, out of the opposition of those forces, and one soon recognizes the confusion reigning within it, and the impossibility of separating out their magnitudes, so that the one has always just as good a claim to be assumed as increasing which in the explanation is assumed as decreasing, and conversely.

3. Transition to Quantity

The qualitative has for its fundamental determination being and immediacy, in which being and nothing are one; limit and determinateness are so identical with the being of the something that with their alteration the something itself vanishes. Because this unity is an immediate one, wherein the difference has disappeared, a difference which is nonetheless in itself at hand within it in the unity of being and nothing, that difference falls, as otherness, outside the unity. This reference to an other, however, contradicts the immediacy in which qualitative determinateness stands. It sublates this otherness, sublates itself, in the infinity of being-for-itself, which is the reference of being-determined to itself, being-determined in itself.

In this equality with itself the qualitative, which at first had the other as something external, has raised itself to its genuine unity. But its determinateness, immediacy, has at the same time vanished.

Being-for-itself is at first only the concept of the infinite reference of the negative to itself, without at the same time containing the negative as a real difference within this unity, so that through this simple unity it itself collapses again into immediacy and has the other as a many outside it. But this many is itself a one, or the one is plurality within itself. The movement of being-for-itself has consisted in realizing itself, or in positing within itself the otherness sublated in it, and thereby in exhibiting itself as identity with itself in otherness.

What is now present, then, is the one which is in unity with itself, yet not immediately, but rather in this, that it refers to its non-being, and thereby to itself; its infinite reference to itself through its non-being. The one is accordingly expanded into unity; otherness has become a limit which, in its negation returned into itself, is no longer determinateness as reference to an other, and hence is an indifferent limit. The immediate unity of the qualitative with itself has thus passed over into unity with itself through its otherness. This unity, in which otherness is taken back into itself and determinateness is thereby indifferent, the sublated quality, is quantity.

Second Section. Magnitude

(Quantity.)

The difference of quantity from quality has just been stated. Quality is the first and immediate determinateness; quantity is determinateness that has grown indifferent towards being, a limit which just as much is no limit.

Being has received the determination of having its simple equality with itself in its otherness and only through the sublating of its otherness.

Otherness and determinateness, insofar as determinateness comes forth again in this sphere, is therefore no longer an immediate, abiding determinateness, but a sublated one, something that does not stand in simple reference to itself but is rather something utterly external to itself. Quantity is determinateness returned infinitely into itself; it is no longer being as reference to an other and as the non-being of an other; determinateness has sublated itself in its otherness, with which it is in unity; and quantity is the indifference of determinateness. — But insofar as determinateness comes on the scene again as distinct from this unity of its own, it comes on as what it is in truth, namely utterly only as in unity with its otherness. As quality it was supposed to be a determinateness that is, standing in simple reference with itself; but as quantity it is determinateness merely sublated, external, not being within itself but in the other.

But at the outset pure quantity must be marked off from itself as determinate quantity, from quantum.

Quantity is first real being-for-itself returned into itself, which as yet has no determinateness upon it; the solid infinite unity.

This passes over, second, into determinateness, but into one which is at the same time none, being merely external. It becomes quantum. Quantum is the determinateness grown indifferent, in other words, determinateness that goes out beyond itself, negating itself; as this otherness of otherness it becomes infinite. Infinite quantum, however, is indifferent determinateness sublated, or it is the reinstatement of quality.

Third, quantum in qualitative form is the quantitative ratio. Quantum merely goes out beyond itself in general; in the ratio, however, it goes out beyond itself into its otherness in such a way that it has its determination in this otherness, and is hence at the same time returned into itself, and the reference to itself is present in its otherness. In the ratio, therefore, quantum has returned into quantity, which is thereby at the same time determined as quality.

At the base of this ratio there still lies the indifference of quantum, or it is a merely formal unity of quality and quantity. The movement of the ratio is its passing over into their absolute unity, into measure.

Remark

In qualitative being the limit appeared at first as something which, distinguished from the being-within-itself of the something, is an external limit, towards which the something itself is indifferent. But this externality of the limit sublated itself at once, and the limit showed itself to be one with the being-within-itself of the something, and to be determinateness. That limit, however, was not yet the quantitative limit; for the being-within-itself of the something is as yet only immediate, and over against it the other maintains itself; it is not yet the infinite being-returned-into-itself of quantity, in which otherness has sublated itself in and for itself. In the case of something, therefore, its limit is essentially its determinateness.

If accordingly we understand by limit the quantitative limit, and a field, for instance, alters its limit, namely the quantitative one, it remains a field afterwards as before. But if its qualitative limit is altered, then this is its determinateness by virtue of which it is a field, and it becomes meadow, forest, and so forth. — A red that is more intense or fainter is always red; but if it changes its quality, it ceases to be red; it would become blue, and so forth. — The true and determinate concept of magnitude, as it has here emerged, that an abiding being lies at the base which is indifferent towards the determinateness that it has, results in every other example as well.

A magnitude is customarily defined as something that admits of being increased or diminished. But to increase means to make something more great, to diminish, to make it less great, and the more in more great, and the less in less great — resolves itself again in this way. There lies in this a difference of magnitude in general from itself, and magnitude would accordingly be that whose magnitude admits of being altered. The definition shows itself to be clumsy for this reason, that within it the very determination is employed which was to be defined. Yet in this imperfect expression the chief moment on which everything turns is not to be mistaken; namely the indifference of the alteration, the fact that its own more and less lies in its very concept; its indifference towards itself.

Chapter 1. Quantity

A. Pure Quantity

1. Magnitude is being-for-itself in sublated form; the repelling one, which conducted itself merely negatively towards another, has passed over into reference with it, conducts itself identically towards the other, and has thereby lost its determination. Being-for-itself has become attraction; but attraction has not itself remained the becoming of the many into one, for the difference of one one from others has likewise vanished and this becoming has passed into rest. Attraction and repulsion are sublated in a unity, or have sunk down to moments. The one is in reference to itself, through attraction, and at the same time to itself as to an other, through repulsion. The one, as this one which has just as much coalesced with the ones that repel one another, has thus acquired, so to speak, a breadth, and has expanded itself into unity. The absolute brittleness of the repelling one has melted into this unity, which, however, since it contains that one, is at the same time determined through the repulsion dwelling within it, and thus as unity of being-outside-itself is unity with itself. In this way attraction has become the moment of continuity in magnitude.

Continuity is therefore simple self-same reference to self, interrupted by no limit and no exclusion, yet not an immediate unity but the unity of the ones that are for themselves. Contained in it, therefore, is the outside-one-another of plurality, but at the same time as one that is undifferentiated, uninterrupted. Plurality is posited in continuity as it is in itself; namely, the many are each of them what the others are, each equal to the other, and plurality is therefore simple, differenceless equality. Continuity is this moment of the self-sameness of being-outside-one-another.

2. Immediately, then, magnitude has in continuity the moment of discreteness. Continuity is self-sameness, but self-sameness of the many, which nevertheless does not become something excluding; and it is repulsion that first stretches this self-sameness out into continuity. Discreteness is therefore for its part a discreteness that flows together, whose ones do not have the void, the negative, for their reference, and do not interrupt continuity, the equality with itself in the many. The difference of repelling is therefore present only as distinguishability.

3. Magnitude, as the unity of these moments, of continuity and discreteness, may be called quantity; for with the expression magnitude what lies nearer to representation is the immediate side of it, and bounded magnitude, the quantum, whereas quantity recalls rather what is reflected and the concept of it.

Quantity is thus being-for-itself as it is in truth. It was the self-sublating referring to itself, a perennial coming-outside-itself. But what is repelled is it itself; repulsion is therefore the generative flowing-forth of its own self. For the sake of the selfsameness of what is repelled, this discerning is unbroken continuity; and for the sake of the coming-outside-itself, this continuity, without being interrupted, is at the same time plurality, which just as immediately remains in its equality with itself.

Remark 1

Pure quantity has as yet no limit, or is not yet quantum; — even insofar as it becomes quantum, it is not limited by the limit, for it consists precisely in this, in not being limited by the limit, in having being-for-itself within it as something sublated. That it is discreteness sublated can also be expressed thus: that quantity is utterly, everywhere within it, the real possibility of the one, but conversely that the one just as utterly is only as something continuous.

For representation devoid of the concept, continuity readily becomes composition, namely an external reference of the ones to one another, in which the one is preserved in its absolute brittleness and exclusion. It has shown itself in the case of the one, however, that of its own self, in and for itself, it goes over into attraction, into its ideality, and that continuity is accordingly nothing external to it but belongs to the one itself and has its ground in its essence. It is this externality of continuity for the ones that atomism in general clings to, and to abandon it and to go into the concept, into the inner, is what constitutes the difficulty for representing.

The concept of pure quantity as against mere representation is what Spinoza, to whom it mattered above all, has in mind when he (Eth. P. I. Prop. XV. Schol.) speaks of quantity in the following way:

Quantitas duobus modis à nobis concipitur, abstrakte scilicet sive superficialiter, prout nempe ipsam imaginamur; vel ut substantia, quod a solo intellectu fit. Si itaque ad quantitatem attendimus, prout in imaginatione est, quod saepe et facilius à nobis fit, reperietur finita, divisibilis et ex partibus conflata, si autem ad ipsam, prout in intellectu est, attendimus, et eam, quatenus substantia est, concipimus, quod difficillime fit, — infinita, unica et indivisibilis reperietur. Quod omnibus, qui inter imaginationem et intellectum distinguere sciverint, satis manifestum erit.

More determinate examples of pure quantity, if such are wanted, are to be had in space and time, also in matter generally, in light and so forth, even in the I; only, as already remarked, what is to be understood by them is not the quantum, or magnitude in general insofar as this points first of all to the quantum. Space, time and so forth are extensions, pluralities, which are a going-outside-of-self, a streaming that nevertheless does not pass over into its opposite, into quality or into the one, but which, as coming-outside-itself, are a perennial self-producing. Space is this absolute being-outside-itself, which is just as much utterly uninterrupted, an otherness-and-again-otherness that is identical with itself; time is an absolute coming-outside-itself, a becoming-nothing that continually is again the becoming-nothing of this passing away; so that this self-generating of non-being amounts just as much to simple equality, to identity with itself.

As concerns matter as quantity, among the seven propositions preserved from Leibniz's first dissertation (l. page of vol. I of his works) there is one bearing on this, the second, which runs as follows: Non omnino improbabile est, materiam et quantitatem esse realiter idem. — In fact these concepts differ no further than in this, that quantity is the pure thought-determination, whereas matter is the same determination in external concrete existence. — To the I as well the determination of pure quantity belongs, since it is an absolute becoming-other, an infinite distancing or repulsion on all sides into the negative freedom of being-for-itself, which yet remains utterly simple continuity. — Those, by contrast, who balk at grasping plurality as simple unity, and who, besides the concept that of the many each is the same as the other, namely one of the many, — for what is spoken of here is not the many as further determined, not green, red and so forth, but the many considered in and for itself, — demand a representation of this unity as well, will find enough of the kind in those continuities, whose simple intuition gives immediately the deduced concept of quantity.

Remark 2

Into the nature of quantity, namely its being this simple unity of discreteness and of continuity, there falls the conflict or the antinomy of the infinite divisibility of space, time, matter and so forth.

This antinomy rests on nothing else than that discreteness has to be maintained no less than continuity. Maintained one-sidedly, discreteness yields as principle the infinite or absolute dividedness, and thus something indivisible; continuity maintained one-sidedly yields, by contrast, infinite divisibility.

Kant's Critique of Pure Reason, as everyone knows, sets out four (cosmological) antinomies, of which the second bears on the opposition constituting the moments of quantity.

An important part of the critical philosophy these Kantian antinomies will always remain; they above all brought down the metaphysics that went before, and they may count as a chief transition into the more recent philosophy. Great as their merit is, however, their presentation is highly imperfect: in part hampered and contorted within itself, in part skewed with respect to its result. Their remarkableness earns them a closer critique, one that will both throw more light on their standpoint and method and release the cardinal point, the one on which everything turns, from the useless form into which it has been squeezed.

Let me note first that Kant meant to lend his four cosmological antinomies a shine of completeness by way of the principle of division which he borrowed from his schema of the categories. Yet the deeper insight into the antinomic, or more truly the dialectical, nature of reason takes every concept whatever as a unity of opposed moments, on which the form of antinomic claims could be conferred. Becoming, existence and so forth, and any other concept, could accordingly yield its own peculiar antinomy, so that as many antinomies might be set out as there are concepts set out.

Kant, moreover, took up the antinomy not within the concepts themselves, but within cosmological determinations, which are an already concrete form. To have the antinomy pure and handle it in its simple concept, the thought-determinations ought to have been taken not in their application to, and their mixing with, the representation of world, space, time, matter and so forth, but ought to have been considered purely by themselves, apart from that concrete material, which contributes neither force nor power here, seeing that they by themselves make up the essence and the ground of the antinomies.

Kant gives this concept of the antinomy, that they are “not sophistical artifices, but contradictions on which reason must of necessity strike (in Kant's own wording);” — a view of importance. — “Reason, once it has seen into the ground of the antinomies' natural shine, is indeed taken in by it no longer, yet it is deceived still.” — For the critical resolution, namely that through what is called the transcendental ideality of the perceived world, arrives at no result beyond making the alleged conflict into something subjective, where it of course persists as the very same shine, that is, is left as unresolved as it was. Their genuine resolution can lie in this alone, that two determinations, being opposed and yet both necessary to one and the same concept, cannot hold good in their one-sidedness, each by itself, but possess their truth only in their sublatedness.

Looked at more closely, the Kantian antinomies hold nothing beyond the quite simple categorical claim put forward for each of the antinomy's two opposed moments. Wrapped about this simple categorical, or properly assertoric, claim, however, is a skewed and twisted scaffolding of ratiocination, by which a shine of proofs is produced and the merely assertoric character of the claim is to be concealed and rendered unrecognizable; as will become plain when they are looked at more closely.

The antinomy pertaining here bears on the alleged infinite divisibility of matter; it is founded on the opposition between the moments continuity and discreteness that the concept of quantity encloses within it.

Its thesis, in Kant's presentation, runs thus:

Each composite substance in the world is composed of simple parts, and there exists nothing anywhere save the simple, or what is put together out of it.

Placed here over against the simple, the atom, is the composite, a determination that lags far behind the steady or continuous. — As for the substrate lent to these abstractions, namely empirical substances in the world, which here signifies nothing more than things as they are perceptible to sense, it has no bearing on what is antinomic itself; space and time might have been taken with equal right. — And since the thesis speaks of composition rather than of continuity, it is properly an analytic or tautological proposition. Its immediate determination is just this, that the composite is not in and for itself but merely something linked externally, and is made up of an other. — But the other of the composite is the simple. Tautological, therefore, is the proposition that the composite is made up of the simple. — Once one asks of what something is made up, what is being called for is an other whose conjunction would constitute that something. Let ink be made up of ink once more, and the sense of the question about being made up has been missed; it goes unanswered. The one question still left is whether that of which we are speaking is to be made up of something or not. The composite, however, is precisely that which is not immediate, not in and for itself, but a mediated, a linked thing, made up of an other. Should it therefore be made up of composites again, the question stands: of what is the composite made up? just as it stood; for it lies in the composite itself. — Take the simple, which is the other of the composite and the very thing being asked after, merely for a relatively-simple that is on its own account composite again, and the answer turns once more into the answer that ink is made up of ink, so that the question is only repeated. Before representation there hovers, as a rule, only this or that composite, for which likewise this or that something would be given as its simple, itself perhaps a composite again on its own account. Here, though, the talk is of the composite as such. Neither, then, can it be asked afresh of what the simple is made up, on the ground that it is itself a composite; for the simple is no composite, but rather the other of the composite.

Kant's proof of the thesis takes, as do all his proofs of the remaining antinomic propositions, the roundabout way, one that will show itself to be quite superfluous, of being apagogic.

“Suppose, he begins, that composite substances were not composed of simple parts; then, were all composition sublated in thought, no composite part would remain, and, there being (by the assumption just laid down) no simple parts either, no simple one, hence nothing whatever would be left over, and accordingly no substance would have been given.” —

The inference is quite correct: where there is nothing but the composite, and one thinks all the composite away, nothing whatever is left over; — that will be granted, but this tautological surplus might have been dispensed with, and the proof might have started straight off with what comes next:

“Either it is impossible for all composition to be sublated in thought, or, once it has been sublated, there must remain something subsisting free of all composition, that is, the simple.”

“In the first case, however, the composite would again not be made up of substances (because in their case composition is but a contingent relation ³ of the substances, with out which these, as beings persisting for themselves, must subsist.) — Since this case contradicts the presupposition, only the second is left: namely that the substantial composite in the world is made up of simple parts.”

That ground, set down by the way in a parenthesis, is in fact the main thing, against which all that has gone before is wholly superfluous. The dilemma runs: either the composite is what abides, or not, but rather the simpl[e]. Were it the former, the composite, that abides, then what abides would not be the substances, since for these composition is only a contingent relation; but substances are what abides, and hence they are simple.

Plainly, without the apagogic detour that ground might have been appended straight away, as its proof, to the thesis: composite substance is made up of simple parts, because composition is a merely contingent relation of the substances, external to them therefore and of no concern to the substances themselves. — Grant that the contingency of composition holds good, and the essence is of course the simple. This contingency, though, on which alone everything turns, is not proved but flatly assumed, assumed in passing and in a parenthesis, as a thing that goes without saying or a side issue. That composition is the determination of contingency and externality does indeed go without saying; but by composition continuity was to be understood, and continuity is surely not to be disposed of in a parenthesis.

Within the apagogic detour, then, we see the very claim turn up that is supposed to issue from it. More briefly the proof may be put like this:

Assume that composite substances were not made up of simple parts. Now all composition can be sublated in thought, (being only a contingent relation;) hence once it is sublated no substances would be left over, unless they were made up of simple parts. Substances, however, we must have, since we assumed them; not everything is to vanish on us, something is to be left over, for we presupposed a persisting thing of that sort and called it substance; this something must therefore be simple.

One more thing belongs to the whole, a look at the concluding proposition; it runs as follows:

“From this it follows at once that the things of the world are without exception simple beings, that composition is in them merely an outer state, and that reason is bound to think the elementary substances as beings that are simple.”

Here the contingency of composition is adduced as a consequence, after having been earlier slipped into the proof parenthetically and put to work there.

Kant protests vigorously that in the conflicting propositions of the antinomy he is not after deceptions, so as to conduct (as the saying goes) a lawyer's proof. What the proof considered is to be charged with is not so much deception as a useless, tortured contortedness, needed only in order to produce the outward shape of a proof and to prevent its standing in full transparency that what was to come forth as a consequence was, in the parenthesis, the hinge of the proof.

The antithesis runs:

No composite thing in the world is composed of simple parts, and there exists nothing simple anywhere within it.

The proof is likewise given an apagogic turn, and is quite as blameworthy as the previous one, though in another way.

“Posit, so it runs, that a composite thing (as substance) is made up of simple parts. Since every external relation, and hence all composition out of substances, is possible only in space, the space it occupies must be made up of as many parts as the composite itself. Now space is made up not of simple parts but of spaces. Each part of the composite must therefore occupy a space.”

“The very first parts of everything composite, however, are simple.”

“Hence the simple occupies a space.”

“Now since everything real that occupies a space encloses within itself a manifold lying outside one another, and is hence composite, composite indeed out of substances, the simple would be a substantial composite. Which is self-contradictory.”

This proof may be called a whole nest (to borrow an expression occurring elsewhere in Kant) of faulty procedure.

To begin with, the apagogic turn is a shine wholly without ground. For the assumption that everything substantial is spatial, whereas space does not consist of simple parts, is a direct claim which makes up the immediate ground of what is to be proved and with which the whole business of proving is already done.

This apagogic proof then starts from the proposition: “that all composition out of substances is an external relation,” only, oddly enough, to forget it again at once. The inference runs on, namely, that composition is possible only in space, that space is not made up of simple parts, and that the real occupying a space is consequently composite. Composition having once been assumed as an external relation, spatiality, as the only element in which composition is held to be possible, is on that very account itself an external relation, one that does not concern the substances and leaves their nature untouched, as little as does everything else that may still be inferred from the determination of spatiality.

It is presupposed, further, that the space into which the substances are here transposed is not made up of simple parts; the ground being that space is an intuition, that is, on Kant's determination, a representation such as can be given only through a single object, and not a discursive concept. — From this Kantian distinction of intuition and concept, as everyone knows, much mischief with intuiting has arisen, and to be spared the labor of comprehending, people have stretched its worth and its domain into infinity. What belongs here is only this, that space, like intuition itself, must at the same time be comprehended; if, that is, one means to comprehend at all. Therewith the question would arise whether space, even were it as intuition simple continuity, would not have to be grasped according to its concept as made up of simple parts, or else space would enter the very antinomy into which substance alone was transposed. Grasped abstractly, the antinomy does in fact concern, as was recalled, quantity in general, and with it space and time no less.

But once the proof has assumed that space is not composed of simple parts, that ought to have been reason enough not to transpose the simple into an element unsuited to the determination of the simple.

In the remark to the proof of the antithesis the critical philosophy's otherwise fundamental representation is expressly brought to bear as well: that only as appearances do we have a concept of bodies, and that as such they cannot but presuppose space, the condition of the possibility of every outer appearance. If by the substances nothing is meant but bodies as we see, feel and taste them and so forth, then what they are in thinking is not really in question; what is at issue is only what sense perceives. Briefly put, then, the proof of the antithesis came to this: the whole experience of our seeing, our feeling and so forth shows us nothing but the composite; not even the best microscopes and the finest blades have yet let us strike upon anything simple. So reason too is not to want to strike upon anything simple.

If, then, we look more exactly at the opposition of this thesis and antithesis and free their proofs of all useless surplus and contortedness, the proof of the antithesis contains, — by transposing the substances into space, — the assertoric assumption of continuity, just as the proof of the thesis contains, — by assuming composition to be the mode in which the substantial is referred, — the assertoric assumption of the contingency of this reference, and with it of the absolute ones. To the severing of quantity's two moments, then, and to their direct assertion insofar as they are severed, the whole antinomy reduces itself. Taken by mere discreteness, substance, matter, space, time and so forth are divided outright, the one being their principle. Taken by continuity, this one is only a sublated one; the dividing remains divisibility, the possibility of dividing remains as possibility, without any actual arrival at the atom. — But so taken, continuity itself contains the moment of the atom; just as that dividedness has sublated every difference among the ones, — for each simple one is that which the other is, — and so likewise contains their absolute likeness and with it their continuity. Because each of the two opposed sides has its other on its own self, and neither admits of being thought apart from the other, it follows that no one of these determinations, taken by itself, possesses truth, but only their unity. Such is the genuine dialectical consideration of them, and such the genuine result.

Far more ingenious and profound than the Kantian antinomy just considered are those dialectical instances of the old Eleatic school, above all the ones bearing on motion, which are likewise founded on the concept of quantity and find their resolution in it. To take them up here as well would carry us too far afield; belonging as they do more closely to the concepts of space and time, they are to be handled where those are treated and in the history of philosophy. The highest honor do they do to the reason of those who devised them; the pure being of Parmenides is their result, for they exhibit the dissolution of all determinate being within itself, and are thus on their own selves the flux of Heraclitus. For that reason they merit a more searching treatment than the usual account of them as being just sophisms; an assertion that clings to perception after the fashion of Diogenes, so plain to ordinary human understanding, who, when a dialectician exhibited the contradiction contained in motion, is said to have strained his reason no further but to have pointed to what the eye sees by silently pacing back and forth, — an assertion and refutation certainly easier to produce than their genuine cognition and resolution, which presupposes an insight into the dialectical nature of the concepts.

Kant's resolution of the antinomy lies in this alone, that reason is not to fly beyond sensuous perception but is to take appearance as it stands. This resolution leaves the content of the antinomy itself lying to one side; it fails to reach the nature of the concept, which is essentially the unity of opposites, each of them, isolated on its own, null and in its own self nothing but the passing over into its other, as here quantity is this unity and therein the truth of the two determinations that make up the antinomy.

B. Continuous and Discrete Magnitude

1. The two moments, continuity and discreteness, are contained in quantity. At first it is their immediate unity. Thus it stands itself under the determination of continuity, and is continuous magnitude.

Or: continuity is at first, to be sure, only one of quantity's moments, and quantity reaches completion only with the other, discreteness. But continuity is just as essentially the whole as well; for only as unity of the discrete is it the cohering, solid unity. Continuity is therefore not moment alone, but no less quantity entire; and this, in that immediate and itself continuous unity, is not so much quantity as magnitude; — hence continuous magnitude.

2. Quantity, taken as immediate, is continuous magnitude. Quantity, however, is in no way something immediate; or, immediacy is a determinateness, a quality belonging to it, whose sublatedness quantity itself is. It therefore passes out of immediacy or indeterminateness into determinateness; but the determinateness immanent to it is the one. — Or: quantity taken immediately, continuous magnitude, is not quantity as such, but quantity as determinate; the genuine determinateness of quantity, however, is the one, and quantity is as discrete magnitude.

Discreteness is in general a moment of quantity, yet is itself the whole of quantity too, since quantity is essentially mediated, negative within itself, standing in the determinateness of the one, an at first indeterminate plurality of ones. Being-outside-one-another is what quantity is, and continuous magnitude is that being-outside-one-another as prolonging itself without negation, as a cohesion self-same within itself. Discrete magnitude is that outside-one-another as non-continuous, as broken off. With this multitude of ones, however, there is not present once more the multitude of atoms and the void. Rather, since discrete magnitude is quantity, the continuity sublated in it is itself continuous. Wherein this continuity in the discrete lies is that the ones are equal to one another, or that they have one and the same unit. Discrete magnitude is accordingly the outside-one-another of the many ones as of the equal, not the many ones simply, but as the many of a unit.