Here I précis the various prefaces and essays at the start of the Science of Logic.
In the opening of the Logic, Hegel sets out his stall in general terms as follows. He distinguishes understanding (Verstand), which he characterises as a pigeon-holing of experience under pre-determined categories, from reason (Vernuft) proper. The work of understanding corresponds largely to the sort of judgments and inferences described above in our description of analytic logic.
Reason however, he thinks, operates on any given understanding and does so in two ways. Firstly, in its negative or dialectical form, it produces criticisms of our previous understanding; but then secondly and more positively, it proposes a new understanding. This second form of reason Hegel calls its speculative form. In other words, Hegel is arguing that processes of conceptual change that are not covered in formal logic as such, are in fact rational processes nonetheless and he proposes to tell us how.
This contrasts with some modern theorists of conceptual change, e.g. Thomas Kuhn's Structure of Scientific Revolutions (1962), which give only a limited role to reason in identifying problems in a given network of concepts, but leave the proposal of solutions to imagination or an ill defined "creativity".
Hegel's ambition is praiseworthy, but there is considerable doubt to what extent he realises it: the sceptic may feel that what he has to say of conceptual change comes out better in his openly historical works. Hegel admits that the concrete parts of his writings shed much light on the abstractions of the Logic.
Hegel also mentions that he considered and rejected the idea of the dialogue form for presenting his ideas on this subject. This is a shame, for it would have added to the clarity of his presentation and arguably would have been appropriate to the subject matter, as conceptual change often comes about through dialogue.
Hegel warns us that he presupposes the identity of thought and being. This may be explained by reference to Descartes, who began his constructive thought with the proposition "I think, therefore I am". As a conscious being in other words, I have assurance at least of my own being: it doesn't make sense to doubt it, for I know that I have to be there doing the doubting. Hegel however, being less drawn to scepticism, goes a little further than this: when I say "it is" (whatever it may be) I am in thought going beyond subjective imaginings and at least thinking (though perhaps mistakenly) about what is outside my own consciousness.
Hegel's subdivision follows roughly the logic of conceptual change outlines above. We start with naive propositions of being (this or that happens to be the case); proceed to dialectical criticisms (this or that appears, but really or essentially things stand differently); and finally the solution is found in a more self-sufficient concept. Thus we have doctrines of being, essence and the concept.
The Doctrine of Being
This section is structured in the familiar Hegelian way, with relatively immediate determinations of quality succeeded by the external comparison of such qualities with each other through quantity and the emergence of measure presented as an outcome or synthesis of these two sets of categories.
One commentator GRG Mure notes that in these essays the transitions have the most resemblance to simply moving from one subject on to another.
The opening section on pure being brings us close to consideration of the ontological proof of God's existence. In the middle section, Hegel shows a considerable knowlege of mathematics, both geometry and algebra and their combination that was begun by Descartes and produces arguments against "the high repute of the progress to infinity".
The concepts here from being on are so general and omnipresent in consciousness though, that arguably little new light can be shed on them by such abstract discussions and the reader may leave the book with an air composed in equal parts of disappointment and bafflement.
The Doctrine of Essence
This book takes a phenomenalist approach to the question of real essences in experience. To take an example, the law of gravity gives us a rule such that, if we know the mass and distance of two bodies, we can predict their motion (using the formula: force = mass x acceleration). One interpretation of this is that gravity must be an "occult" (hidden) quality or "force" behind experience, but Hegel argues that all such qualities have to be seen ultimately as properties of experience itself, although they indicate that experience is not simply a conjunction of accidental atoms (whether of sensation or matter) and properties.
He gives illustrations with equal weight from mental life, as mental dispositions (e.g. generosity) also have to be manifested if we are to judge of their presence.
As usual, he gives a tour of the concepts that are used, from illusion through appearance to reality, in talking about this aspect of experience. Some commentators have felt that the content of the argument does not justify the length of the treatment, but on the other hand the argument does have a content and at least some validity.
In addition, the style of argument will be relaticely familiar to the reader of empiricist philosophy. Saul Kripke's Naming and Necessity (1975) helped to reintroduce essentialist ideas inot contemporary debate, though for much of the twentieth century these were a subject of derision in Anglophone academe.
The Doctrine of the Concept
This book has a dog's breakfast of a structure (unless you know better) and Hegel acknowledges that he has had insufficient time to work on it.
It begins with a lengthy recapitulation from the "subjective" standpoint of the material presented "objectively" in the previous two books. By this he means that he speaks in terms of our mental concepts, judgments and inferences (e.g. our judgment "A exists" rather than about existence as such), readdressing the content already covered.
However, having reintroduced the cognitive subject, he takes up again the idea of the concepts he has introduced as a characterisation of experience as a whole. The book concludes with a highly abstract vindication of the idea of God as Spirit.