Hegel’s Science of Logic
The many ones have affirmative being; their determinate being or relation to one another is a non-relation, is external to them — the abstract void. But they themselves are now this negative relation to themselves as to affirmatively present others — the demonstrated contradiction, infinity posited in the immediacy of being. Thus repulsion now simply finds immediately before it that which is repelled by it. In this determination repulsion is an exclusion; the one repels from itself only the many ones which are neither generated nor posited by it. This mutual or all-round repelling is relative, is limited by the being of the ones.
The plurality is, in the first place, non-posited otherness, the limit is only the void, only that in which the ones are not. But in the limit they also are; they are in the void, or their repulsion is their common relation.
This mutual repulsion is the posited determinate being of the many ones; it is not their being-for-self, for according to this they would be differentiated as many only in a third, but it is their own differentiating which preserves them. They negate one another reciprocally, posit one another as being only for-one. But at the same time they equally negate this being only for-one; they repel this their ideality and are. Thus the moments which in ideality are absolutely united are separated. The one is, in its being-for-self, also for-one, but this one for which it is is its own self; its differentiation of itself is immediately sublated. But in plurality the differentiated one has a being; the being-for-one as determined in exclusion is, consequently, a being-for-other. Each is thus repelled by an other, is sublated and made into that which is not for itself but for-one, and that another one.
The being-for-self of the many ones shows itself, therefore, as their self-preservation through the mediation of their mutual repulsion in which they mutually sublate themselves and each posits the others as a mere being-for-other; but the self-preservation at the same time consists in repelling this ideality and in positing the ones as not being for-an-other. This self-preservation of the ones through their negative relation to one another is, however, rather their dissolution.
The ones not only are, but they maintain themselves through their reciprocal exclusion. Now in the first place that which should enable the ones to maintain their diversity in opposition to their being negated is their being, in fact, their being-in-itself as opposed to their relation-to-other; this being-in-itself is that hey are ones. But this is what they all are; they are in their beingin-itself the same instead of this latter being the fixed point of their diversity. Secondly, their determinate being and their relation to one another, that is, their positing of themselves as ones, is the reciprocal negating of themselves; but this likewise is one and the same determination of them all, through which then they rather posit themselves as identical; similarly, because they are in themselves the same, their ideality, instead of being posited through others, is their own, and they therefore repel it just as little. Consequently, as regards both their being and their positing, they are only one affirmative unity.
This reflection that the ones, determined both as simply being and as inter-related, show themselves to be one and the same and indistinguishable, is a comparison made by us. But we have also to see what is posited in them in their interrelatedness. They are — this is presupposed in this inter-relatedness — and they are only in so far as they reciprocally negate one another and at the same time hold themselves aloof from this their ideality, their negatedness, that is, negate this reciprocal negating. But they are only in so far as they negate; consequently, since this their negating is negated, their being is negated. It is true that since they are, they would not be negated by this negating, which for them is only something external; this negating by the other rebounds off them and touches only their surface. And yet it is only through this negating of the others that the ones return into themselves: they are only as this mediation, and this their return is their self-preservation and their being-for-self. Since their negating is ineffectual because of the resistance offered by the ones either as simply affirmative or as negating, they do not return into themselves, do not preserve themselves, and so are not.
The observation was made above that the ones are the same, each of them is a one like the other. This is not only a relating of them by us, an external bringing of them together; on the contrary, repulsion is itself a relating; the one which excludes the ones relates itself to them, to the ones, that is, to its own self. Hence the negative relationship of the ones to one another is only a going-together-with-self. This identity into which their repelling passes over is the sublating of their diversity and externality which they, as excluding, ought rather to maintain relatively to one another.
This positing of themselves by the many ones into a single one is attraction.
Remark: The unity of the One and the Many
Self-subsistence pushed to the point of the one as a being-for-self is abstract, formal, and destroys itself. It is the supreme, most stubborn error, which takes itself for the highest truth, manifesting in more concrete forms as abstract freedom, pure ego and, further, as Evil. It is that freedom which so misapprehends itself as to place its essence in this abstraction, and flatters itself that in thus being with itself it possesses itself in its purity. More specifically, this self-subsistence is the error of regarding as negative that which is its own essence, and of adopting a negative attitude towards it. Thus it is the negative attitude towards itself which, in seeking to possess its own being destroys it, and this its act is only the manifestation of the futility of this act. The reconciliation is the recognition that the object of this negative attitude is rather its own essence, and is only the letting go of the negativity of its being-for-self instead of holding fast to it.
It is an ancient proposition that the one is many and especially that the many are one. We may repeat here the observation that the truth of the one and the many expressed in propositions appears in an inappropriate form, that this truth is to be grasped and expressed only as a becoming, as a process, a repulsion and attraction-not as being, which in a proposition has the character of a stable unity. We have already mentioned and recalled the dialectic of Plato in the Parmenides concerning the derivation of the many from the one, namely, from the proposition: the one is. The inner dialectic of the Notion has been stated; it is easiest to grasp the dialectic of the proposition, that the many are one, as an external reflection; and it may properly be grasped externally here inasmuch as the object too, the many, are mutually external. It directly follows from this comparison of the many with one another that any one is determined simply like any other one; each is a one, each is one of the many, is by excluding the others — so that they are absolutely the same, there is present one and only one determination. This is the fact, and all that has to be done is to grasp this simple fact. The only reason why the understanding stubbornly refuses to do so is that it has also in mind, and indeed rightly so, the difference; but the existence of this difference is just as little excluded because of the said fact, as is the certain existence of the said fact in spite of the difference. One could, as it were, comfort understanding for the naive manner in which it grasps the fact of the difference, by assuring it that the difference will also come in again.
Repulsion is the self-differentiating of the one, at first into many, whose negative relationship is without effect because they presuppose one another as affirmatively present; it is only the ought-to-be of ideality. In attraction, however, ideality is realised. Repulsion passes over into attraction, the many ones into one one. Both repulsion and attraction are in the first place distinct from each other, the former as the reality of the ones, the latter as their posited ideality. The relation of attraction to repulsion is such that the former has the latter for presupposition. Repulsion provides the material for attraction. If there were no ones there would be nothing to attract; the conception of a perpetual attraction, of an absorption of the ones, presupposes an equally perpetual production of them. Spatial attraction as pictorially conceived makes the flow of attracted ones proceed uninterruptedly; in place of the atoms which vanish in the centre of attraction, another multitude comes forth from the void, and so on to infinity if one wishes. If attraction were conceived as accomplished, the many being brought to the point of the one one, then there would be present only an inert one and no longer any attraction. The ideality present in attraction still also bears within itself the determination of the negation of itself, the many ones of which it is the relatedness: attraction is inseparable from repulsion.
In the first place, attraction belongs equally to each of the many ones as immediately present; none has any precedence over another; this would result in an equilibrium in attraction, or, strictly speaking, an equilibrium of attraction and repulsion itself, and an inert state of rest in which ideality would have no determinate being. But there can be no question here of a precedence of such a one over another, for this would presuppose a specific difference between them; rather is attraction the positing of the immediately present undifferentiatedness of the ones. It is only attraction itself that is a positing of a one distinct from other ones; these are only immediate ones which should maintain themselves through repulsion; but through their posited negation arises the one of attraction, which is consequently determined as mediated, the one posited as one. The first ones, as immediate, do not in their ideality return into themselves but have this ideality in another one.
The one one, however, is the realised ideality, posited in the one; it is attraction through the mediation of repulsion, and it contains this mediation within itself as its determination. Thus it does not absorb the attracted ones into itself as into a centre, that is, it does not sublate them abstractly. Since it contains repulsion in its determination, this latter at the same time preserves the ones as many in it; through its attracting, so to speak, it acquires something for itself, obtains an extension or filling. There is thus in it the unity of repulsion and attraction in general.
The difference of the one and the many is now determined as the difference of their relation to one another, with each other, a relation which splits into two, repulsion and attraction, each of which is at first independent of the other and stands apart from it, the two nevertheless being essentially connected with each other. Their as yet indeterminate unity is to be more precisely ascertained. ®
Repulsion, as the basic determination of the one, appears first and as immediate, like its ones which although generated by repulsion are yet also posited as immediate. As such, repulsion is indifferent to attraction which is externally added to it as thus presupposed. Attraction on the other hand is not presupposed by repulsion in such a manner that the former is supposed to have no part in the positing and being of the latter, that is, as if repulsion were not already in its own self the negation of itself and the ones were not already in themselves negated. In this way we have repulsion abstractly on its own account and, similarly, attraction relatively to the ones as affirmatively present, has the side of an immediate determinate being and comes to them as an other.
If repulsion is thus taken merely by itself, then it is the dispersion of the many ones into somewhere undetermined, outside the sphere of repulsion itself; for repulsion is this, to negate the interrelatedness of the many: the absence of any relation between them is the determination of the many taken abstractly. But repulsion is not merely the void; the ones, as unrelated, do not repel or exclude one another, this constitutes their determination. Repulsion is, although negative, still essentially relation; the mutual repulsion and flight is not a liberation from what is repelled and fled from, the one as excluding still remains related to what it excludes. But this moment of relation is attraction and thus is in repulsion itself; it is the negating of that abstract repulsion according to which the ones would be only self-related affirmative beings not excluding one another.
In starting, however, with the repulsion of the determinately present ones and so, too, with attraction posited as externally connected with it, the two determinations although inseparable are held apart as distinct; but it has been found that not merely is repulsion presupposed by attraction, but equally, too, there is a reverse relation of repulsion to attraction, and the former equally has its presupposition in the latter.
As thus determined they are inseparable and at the same time each is determined as an ought and a limitation relatively to the other. Their ought is their abstract determinateness in the form of the in-itself, but with this determinateness each is simply directed away from itself and relates itself to the other, and thus each is through the mediation of the other as other; their self-subsistence consists in the fact that in this mediation each is posited for the other as a different determining: repulsion as the positing of the many, attraction as the positing of the one, the latter as at the same time a negation of the many, and the former as a negation of their ideality in the one, so that attraction, too, is attraction only through the mediation of repulsion, just as repulsion is repulsion through the mediation of attraction. But the fact that in this interdependence the mediation of each through the other is rather negated, each of these determinations being a self-mediation, becomes evident after a closer consideration of them and brings them back to the unity of their Notion.
In the first place, that each presupposes itself, is related only to itself in its presupposition, this is already implied in the relationship between repulsion and attraction in their initially still relative character.
Relative repulsion is the mutual repelling of the present many ones which are supposed to be immediately given. But that there are many ones, this is repulsion itself; any presupposition which it might have is only its own positing. Further, the determination of being which might belong to the ones apart from the circumstance that they are posited — whereby they would be already there-belongs likewise to repulsion. The repelling is that whereby the ones manifest and maintain themselves as ones, whereby they are as such. Their being is repulsion itself, which is thus not a relative determinate being over against another such, but relates itself simply and solely to its own self.
Attraction is the positing of the one as such, of the real one, in contrast to which the many in their determinate being are determined as only ideal [ideell] and as vanishing. Attraction thus directly presupposes itself — in the determination, namely, of the other ones as ideal, which ones are otherwise supposed to be for themselves, repelling others, and therefore also any attracting one. Ideality, as opposed to this determination of repulsion, does not belong to the ones only through the relation to attraction; on the contrary, it is presupposed, it is the ideality inherent in the ones in that, as ones — including the one conceived as attracting — they are not distinguished from one another, are one and the same.
Further, this self-presupposing of the two determinations each for itself, means that each contains the other as a moment within it. The self-presupposing as such is the one's positing of itself in a one as the negative of itself-repulsion; and what is therein presupposed is the same as that which presupposes-attraction. That each is in itself only a moment, is the transition of each out of itself into the other, the self-negating of each in itself and the self-positing of each as its own other. The one as such, then, is a coming-out-of-itself, is only the positing of itself as its own other, as many; and the many, similarly, is only this, to collapse within itself and to posit itself as its other, as one, and in this very act to be related only to its own self, each continuing itself in its other. Thus there is already present in principle (an sich) the undividedness of the coming-out-of-itself (repulsion) and the self-positing as one (attraction). But in the relative repulsion and attraction, which presuppose immediate, determinates existent ones, it is posited that each is in its own self this negation of itself and is thus also the continuity of itself in its other. The repulsion of the determinately existent ones is the self-preservation of the one through the mutual repulsion of the others, so that (1) the other ones are negated in it-this is the side of its determinate being or of its being-for-other; but this is thus attraction as the ideality of the ones; and (2) the one is in itself, without relation to the others; but not only has being-in-itself as such long since passed over into being-for-self, but the one in itself, by its determination, is the aforesaid becoming of many ones. The attraction of the determinately existent ones is their ideality and the positing of the one, in which, accordingly, attraction as a negating and a generating of the one sublates itself, and as a positing of the one is in its own self the negative of itself, repulsion.
With this, the development of being-for-self is completed and has reached its conclusion. The one as infinitely self-related — infinitely, as the posited negation of negation — is the mediation in which it repels from itself its own self as its absolute (that is, abstract) otherness, (the many), and in relating itself negatively to this its non-being, that is, in sublating it, it is only self-relation; and one is only this becoming in which it is no longer determined as having a beginning, that is, is no longer posited as an immediate, affirmative being, neither is it as result, as having restored itself as the one, that is, the one as equally immediate and excluding; the process which it is posits and contains it throughout only as sublated. The sublating, at first determined as only a relative sublating of the relation to another determinately existent one-a relation which is thus itself not an indifferent repulsion and attraction — equally displays itself as passing over into the infinite relation of mediation through negation of the external relations of the immediate, determinately existent ones, and as having for result that very process of becoming which, in the instability of its moments, is the collapse, or rather going-together-with-itself, into simple immediacy. This being, in the determination it has now acquired, is quantity.
A brief survey of the moments of this transition of quality into quantity shows us that the fundamental determination of quality is being and immediacy, in which limit and determinateness are so identical with the being of something, that with its alteration the something itself vanishes; as thus posited it is determined as finite. Because of the immediacy of this unity, in which the difference has vanished but is implicitly present in the unity of being and nothing, the difference as otherness in general falls outside this unity. This relation to other contradicts the immediacy in which qualitative determinateness is self-relation. This otherness sublates itself in the infinity of being-for-self which makes explicit the difference (which in the negation of the negation is present in it) in the form of the one and the many and their relations, and has raised the qualitative moment to a genuine unity, that is, a unity which is no longer immediate but is posited as accordant with itself.
This unity is, therefore, [a] being, only as affirmative, that is immediacy, which is self-mediated through negation of the negation; being is posited as the unity which pervades its determinatenesses, limit, etc., which are posited in it as sublated; [b] determinate being: in such determination it is the negation or determinateness as a moment of affirmative being, yet determinateness no longer as immediate, but as reflected into itself, as related not to an other but to itself; a being determined simply in itself-the one; the otherness as such is itself a being-for-self; [c] being-for-self, as that being which continues itself right through the determinateness and in which the one and the intrinsic determinedness is itself posited as sublated. The one is determined simultaneously as having gone beyond itself, and as unity; hence the one, the absolutely determined limit, is posited as the limit which is no limit, which is present in being but is indifferent to it.
Remark: The Kantian Construction of Matter - next section
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