Hegel’s Second Book of the Objective Logic is summarised in the introductory part to his Subjective Logic
The Doctrine of the Notion
The Notion in General
What the nature of the Notion is, can no more be stated offhand than can the Notion of any other object. It might perhaps seem that, in order to state the Notion of an object, the logical element were presupposed and that therefore this could not in turn have something else for its presupposition, nor be deduced; just as in geometry logical propositions as applied to magnitude and employed in that science, are premised in the form of axioms, determinations of cognition that have not been and cannot be deduced. Now although it is true that the Notion is to be regarded, not merely as a subjective presupposition but as the absolute foundation, yet it can be so only in so far as it has made itself the foundation. Abstract immediacy is no doubt a first; yet in so far as it is abstract it is, on the contrary mediated, and therefore if it is to be grasped in its truth its foundation must first be sought. Hence this foundation, though indeed an immediate, must have made itself immediate through the sublation of mediation.
From this aspect the Notion is to be regarded in the first instance simply as the third to being and essence, to the immediate and to reflection. Being and essence are so far the moments of its becoming; but it is their foundation and truth as the identity in which they are submerged and contained. They are contained in it because it is their result, but no longer as being and essence. That determination they possess only in so far as they have not withdrawn into this their unity.
Objective logic therefore, which treats of being and essence constitutes properly the genetic exposition of the Notion. More precisely, substance is already real essence, or essence in so far as it is united with being and has entered into actuality. Consequently, the Notion has substance for its immediate presupposition; what is implicit in substance is manifested in the Notion. Thus the dialectical movement of substance through causality and reciprocity is the immediate genesis of the Notion, the exposition of the process of its becoming. But the significance of its becoming, as of every becoming is that it is the reflection of the transient into its ground and that the at first apparent other into which the former has passed constitutes its truth. Accordingly the Notion is the truth of substance; and since substance has necessity for its specific mode of relationship, freedom reveals itself as the truth of necessity and as the mode of relationship proper to the Notion.
The progressive determination of substance necessitated by its own nature, is the positing of what is in and for itself. Now the Notion is that absolute unity of being and reflection in which being is in and for itself only in so far as it is no less reflection or positedness, and positedness is no less being that is in and for itself. This abstract result is elucidated by the exposition of its concrete genesis; that exposition contains the nature of the Notion whose treatment it must have preceded. The chief moments of this exposition (which has been given in detail in the Second Book of the Objective Logic) can therefore only be briefly summarised here.
Substance is the absolute, the actuality that is in and for itself in itself as the simple identity of possibility and actuality, absolute essence containing all actuality and possibility within itself; and for itself, being this identity as absolute power or purely self-related negativity. The movement of substantiality posited by these moments consists in the following stages:
1. Substance, as absolute power or self-related negativity, differentiates itself into a relationship in which what were at first only simple moments are substances and original presuppositions. Their specific relationship is that of a passive substance, of the original immediacy of the simple inwardness or in-itself which, powerless to posit itself, is only an original positedness and of an active substance, the self-related negativity which as such has posited itself in the form of an other and relates itself to this other. This other is simply the passive substance which the active substance through its own originative power has presupposed for itself as condition. This presupposing is to be understood in the sense that the movement of substance itself is, in the first instance, under the form of one of the moments of its Notion, the in-itself, and the determinateness of one of the substances standing in relationship is also the determinateness of this relationship itself.
2. The other moment is being-for-self, which means that the power posits itself as self-related negativity, thereby sublating again what was presupposed. The active substance is the cause; it acts, that is, it now posits, whereas previously it only presupposed; so that (a) to the power is now added the illusory show of power, to the positedness the illusory show of positedness. What in the presupposition was original, becomes in causality, through the relation to an other, what it is in itself; the cause produces an effect, and that, too, in another substance; it is now power in relation to an other and thus appears as a cause, but is a cause only in virtue of this appearing. (b) The effect enters the passive substance, whereby it now also appears as a positedness, but is a passive substance only as such positedness.
3. But there is still more present in this than only this appearance, namely: (a) the cause acts on the passive substance and alters its determination; but this is positedness, there is nothing else in it to alter; the other determination, however, that it receives is causality; the passive substance therefore becomes cause, power and activity: (b) the effect is posited in it by the cause; but that which is posited by the cause is the cause itself which, in acting, is identical with itself; it is this that puts itself in the place of the passive substance. Similarly, with regard to the active substance, (a) the action is the translation of the cause into the effect, into the other of the cause, into positedness, and (b) the cause reveals itself in the effect as what it is; the effect is identical with the cause, is not an other-; thus the cause in acting reveals the posited being as that which the cause essentially is. Each side, therefore, in both its identical and negative relation to the other becomes the opposite of itself, so that the other, and therefore also each, remains identical with itself. But the identical and the negative relations are both one and the same; substance is self-identical only in its opposite and this constitutes the absolute identity of the substances posited as a duality. Active substance, through the act of positing itself as the opposite of itself, an act which is at the same time the sublating of its presupposed otherness, of passive substance, is manifested as cause or originative substantiality. Conversely, through being acted on, posited being is manifested as posited, the negative as negative, and therefore passive substance as self-related negativity, the cause meeting in this other simply and solely with its own self. Through this positing, then, the presupposed or implicit originativeness becomes explicit or for itself; yet this being that is in and for itself is such only in so far as this positing is equally a sublating of what was presupposed; in other words absolute substance has returned to itself and so become absolute, only out of and in its positedness. Hence this reciprocity is the appearance that again sublates itself, the revelation that the illusory being of causality in which the cause appears as cause, is illusory being. This infinite reflection-into-self, namely, that being is in and for itself only in so far as it is posited, is the consummation of substance. But this consummation is no longer substance itself but something higher, the Notion, the subject. The transition of the relation of substantiality takes place through its own immanent necessity and is nothing more than the manifestation of itself, that the Notion is its truth, and that freedom is the truth of necessity.