To a great extent the whole of the Objective Logic of Hegel comes down to an understanding of Reflection (the first subdivision of the Doctrine of Essence).
In inorganic nature, reflection is the process of things reproducing, under the influence of other things, traces or imprints of the things exercising that influence; in organic nature, reflection is an active process, such as in the adaptation of animals to their environment or the irritability of plants and other organisms. Here, properties in the organism which are the outcome of a long process of adaptation by the species are manifested actively by the individual in the immediate influence of other bodies in the environment the like of which have been present during this period of development. The concept of reflection, as the correspondence of mental images with the material world which is the source of those images, is the basis of the materialist approach to cognition.
Hegel's analysis of reflection in terms of the correspondence between phenomena and their essence is founded on his critique of formal logic. As such, an understanding of reflection binds together the Objective Logic (Being and Essence) and the Subjective Logic, The Doctrine of the Notion, in which dialectics is developed as a systematic method of elaboration and critique of knowledge.
It is often the case in reading The Logic, the key to understanding a section is found in the last paragraph of the preceding section:
§111n (last section of Doctrine of Being)
Measure is implicitly Essence; and its process consists in realising what it is implicitly. The ordinary consciousness conceives things as being, and studies them in quality, quantity, and measure. These immediate characteristics, however, soon show themselves to be not fixed but transient; and Essence is the result of their dialectic.
Being comes to us as a series of qualities passing one after another, and quantitative change in qualities. Relative stability emerges in the form of Measure. Measure is the dialectic of quantity and quality which passes into the recognition of something. This "recognition", or "reflection" is the unity of the "ascending" dialectic of Measure with the mediated "descent" to immediacy of past Being, in the form of Notions or mediated knowledge.
Hegel introduces the Doctrine of Essence in The Shorter Logic as follows:
§ 112
The terms in Essence are always mere pairs of correlatives, and yet not absolutely reflected in themselves: hence in essence the actual unity of the notion is not yet realised, but only postulated by reflection. Essence - which is Being coming into mediation with itself through the negativity of itself - is self-relatedness, only in so far as it is relation to an Other - this Other however coming to view at first not as something which is, but as postulated and hypothesised.
Being has not vanished: but, firstly, Essence, as simple self-relation, is Being, and secondly as regards its one-sided characteristic of immediacy, Being is deposed to a mere negative, to a seeming or reflected light - Essence accordingly is Being thus reflecting light into itself.
At this moment of reflection we have the meeting of two different things, which Hegel refers to as being "postulated" (my emphasis). But Being meets not a stranger, but itself, as an Other, which is mediated Being. It is at this point that we have the really "hard" problems of the theory of knowledge, the point at which Kant, for example, falls into scepticism, the point beyond which logic cannot go without grasping the unity of opposites as the essence of a concept.
This identity [reflection-into-self], as it descended from Being, appears in the first place only charged with the characteristics of Being, and referred to Being as to something external. This external Being, if taken in separation from the true Being (of Essence), is called the Unessential. But that turns out to be a mistake. Because Essence is Being-in-self, it is essential only to the extent that it has in itself its negative, i.e. reference to another, or mediation. Consequently, it has the unessential as its own proper seeming (reflection) in itself. But in seeming or mediation there is distinction involved: and since what is distinguished (as distinguished from identity out of which it arises, and in which it is not, or lies as seeming) receives itself the form of identity, the semblance [or Illusory Being] is still not in the mode of Being, or of self-related immediacy. [Shorter Logic, § 114]
When we at first recognise something, the semblance of the thing shows itself out of the infinite richness of immediate perception. With this "hypothesis", we abstract that image from everything else, which is assumed to be "unessential". It is a "mistake", because the inherent movement and contradiction implicit in Being is the "truth of Being", i.e. Essence, and will show itself. Thus thought cannot "draw a boundary around" this thing, and deal with it as something whose contradiction lies only "externally", in the relativity of perception. On the contrary, Being itself is inherently and implicitly contradictory. The unessential is essence's own unessential, and proves to be equally essential as unessential.
[Essence] is also the sphere in which the contradiction, still implicit in the sphere of Being, is made explicit.
In the Shorter Logic (1830), Hegel heads the first Section of Essence "A. ESSENCE AS GROUND OF EXISTENCE", and the first Chapter of that section: "(a) The pure principle or categories of Reflection". It is in this chapter that Hegel develops the concept of contradiction as the essence of a concept, its Ground, by a dialectical unfolding of the concept of Identity through a series of stages in which Identity is successively transformed to reveal the concepts of Difference, Opposition, Contradiction and finally Ground. In the course of this development, Hegel makes a critique of formal logic. I think that this critique of formal logic has led to some misunderstandings and I will deal with formal logic separately below, in the form of a reassertion of the relative truth of formal logic and its proper relation to and place in dialectics.
Identity is the affirmative connection between two different moments of perception which asserts that they are one and the same and specifically denies that they are in fact "two different moments of perception" at all. It is also the assertion that in a proposition being true, the denial of that proposition is specicallly excluded:
The maxim of Identity, reads: Everything is identical with itself, A = A: and negatively, A cannot at the same time be A and Not-A.
A moment's reflection will show both that consciousness could not take a single step forward without the conviction of identity but equally that the "maxim of Identity" is wrong, that is, that it is a limited, finite truth that will fall over at the first hurdle.
If we recognise something, and say, for example: "Ah! It's a demonstration coming down the road", i.e. not a riot, for example, then we continue to perceive the event, much judgements, etc., on the basis of the same, past perception. We cannot time after time, instant after instant re-look at the approaching crowd. (We can and must of course - that is the philosophy of Being, and it has its relative truth, too, but we have to move forward, we need to know what it is in truth and must move beyond mere immediacy).
Thus we again and again assert the maxim of identity. "Ah!", the formal logical pedant would say, "A = A refers only to what is was at one particular moment, not a moment later". True, but as Hegel replies, in that interpretation A = A is the merest tautology which tells us nothing about thought or perception, and illustrates this with the contrast between the A's to the left or right of the =-sign. Thus, the law and concept of Identity which Hegel is dealing with here is indeed the same concept as "A = A" in formal logic, but he is dealing with it differently. He has disclosed both its truth and its essential, inherent contradiction, and operates with it, not by rigidly sticking to it, but by unfolding out of it its negation.
And this law of identity relfects and objective character of the world - it's relative stability. It is true and valid to perceive and think in this way, on the basis of the maxim of identity. But ...
It is a universal law of the objective world and thus the world of thought, that "Identity comes to Difference" ...
"A = A" only makes sense even in the strictest and valid application of formal logic if the first A is indeed not the second A, it is impossible to utter the law other than by making such a distinction!
To ask 'How Identity comes to Difference' assumes that Identity as mere abstract Identity is something of itself, and Difference also something else equally independent ... Diversity has, like Identity, been transformed into a maxim: 'Everything is various or different': or 'There are no two things completely like each other'.
This "Maxim of Variety", which Hegel attributes to Leibnitz, is indeed a universal, objective law of nature and thought, and I am not aware of any discovery in micro-physics that excludes it either. Hegel shows not just this, but that the Law of Variety (or Diversity) is implicit in the Law of Identity!
Likeness is an identity only of those things which are not the same, not identical with each other: and Unlikeness is a relation of things alike. The two therefore do not fall on different aspects or points of view in the thing, without any mutual affinity, but one throws light into the other. Variety thus comes to be reflexive difference or difference (distinction) implicit and essential, determinate or specific difference. [Shorter Logic § 118]
... and further discovers within the "Maxim of Diversity", or the concepts of likeness and unlikeness, the deeper truth of essential difference or "Opposition":
When we hold to that moment of "unlikeness", when we seek to define it or say just what it is, what makes this demonstration not just a demonstration but a "feeder march", for example, we are able to "make a point of" this unlikeness, we find that this unlikeness is not just accidental or passing, but essential:
Difference implicit is essential difference, the Positive and the negative: and that is this way. The Positive is the identical self-relation in such a way as not to be the Negative, and the Negative is the different by itself so as not to be the Positive. Thus either has an existence of its own in proportion as it is not the other. The one is made visible in the other, and is only in so far as that other is. Essential difference is therefore Opposition; according to which the different is not confronted by any other but by its other. That is, either of these two (Positive and Negative) is stamped with a characteristic of its own only in its relation to the other: the one is only reflected into itself as it is reflected into the other. And so with the other. Either in this way is the other's own other.
Difference implicit or essential gives the maxim, Everything is essentially distinct; or, as it has also been expressed, Oof two opposite predicates the one only can be assigned to anything, and there is no third possible. This maxim of Contrast or Opposition most expressly controverts the maxim of identity
Having shown that the maxim (or judegement) of Opposition expressly controverts the maxim (or judgement) of identity, Hegel brings the two together: it is a demonstration and it is a feeder march, but these are two different things. The feeder march is not just a group of people making their way to the City Square, and the demonstration has quite a distinct content from the demands it carries.
We can begin to see how diaelctics is the logic of reality, of the world of concrete things, really connected, abstracted by thought yes, but thought which is perceiving reality cannot rest, but is driven deeper and deeper, and comes to contradiction: it not only both is and is not, but is and is not essentially:
Instead of speaking by the maxim of Excluded Middle (which is the maxim of abstract understanding) we should rather say: Everything is opposite. Neither in heaven nor in Earth, neither in the world of mind nor of nature, is there anywhere such an abstract 'either-or' as the understanding maintains. Whatever exists is concrete, with difference and opposition in itself. The finitude of things will then lie in the want of correspondence between their immediate being, and what they essentially are. ... its only being consists in its relation to its other. .... Contradiction is the very moving principle of the world: and it is ridiculous to say that contradiction is unthinkable. The only thing correct in that statement is that contradiction is not the end of the matter, but cancels itself. But contradiction, when cancelled, does not leave abstract identity; for that is itself only one side of the contrariety. The proximate result of opposition (when realised as contradiction) is the Ground
When we have grasped the specific contradiction which makes the thing what it really is, then we have perceived it, we have recognised what it is. Not before then. This whole development of the Logic is required to prove this, but in this development of Reflection from Identity to Ground, Hegel has focussed on the identity of Being and the Notion and found contradiction at the heart and kernel of the matter. Being can find its Other only in Notions which have their Ground in this dialectical unfolding which leads to inherent, essential contradiction.
The maxim of Ground runs thus: Everything has its Sufficient Ground: that is, the true essentiality of any thing is not the predication of it as identical with itself, or as different (various), or merely positive, or merely negative, but as having its Being in an other, which, being the self-same, is its essence.
Before moving to a consideration of the place of formal logic in dialectics, I ask the reader to re-call tehfollowing passage from The Doctrine of Being in The Shorter Logic:
In the history of philosophy the different stages of the logical idea assume the shape of successive systems, each based on a particular definition of the Absolute. As the logical Idea is seen to unfold itself in a process from the abstract to the concrete, so in the history of philosophy the earliest systems are the most abstract, and thus at the same time the poorest. The relation too of the earlier to the later systems of philosophy is much like the relation of the corresponding stages of the logical Idea: in other words, the earlier are preserved in the later: but subordinated and submerged. This is the true meaning of a much misunderstood phenomenon in the history of philosophy - the refutation of one system by another, of an earlier by a later. Most commonly the refutation is taken in a purely negative sense to mean that the system refuted has ceased to count for anything, has been set aside and done for. Were it so, the history of philosophy would be, of all studies, most saddening, displaying, as it does, the refutation of every system which time has brought forth. Now although it may be admitted that every philosophy has been refuted, it must be in an equal degree maintained that no philosophy has been refuted. And that in two ways. For first, every philosophy that deserves the name always embodies the Idea: and secondly, every system represents one particular factor or particular stage in the evolution of the Idea. The refutation of a philosophy, therefore, only means that its barriers are crossed, and its special principle reduced to a factor in the completer principle that follows.