Hegel is alive and well in Continental and Postmodern thought. Basically the whole of Continental Philosophy can be seen as footnotes to Hegel, just like Western philosophy can be seen as a footnote to Plato as Whitehead said.
Hegel created his dialectics based on the form of dialectics advocated by the Skeptics like Sextus Empiricus. He refined this into his Logic via his Phenomenology. The whole idea was to get time into philosophy either by looking at the history of the development of consciousness, or by finding a method of reasoning that was not static like normal logic in which the proofs are eternal once produced but the formalism disconnects logic from the actual world where we live with contraction. Basically as Zeno showed if something moves there is contradiction, so Hegel wanted to model the movement of thought internally just like Plato modeled it in Dialogues.
What does not get mentioned in any books I have read on Dialectics and I have tried to read them all, is that Hegel also developed Trialectics with respect to Work as the door into Spirit, and that was modeled on his ideas of Trinitarianism influenced by Jakob Boehm. Once we understand that dialectics evolves into Trialities (three way complementaries) then we can connect the thought of Hegel to that of CS Peirce, who developed his paragmaticism as a reaction to idealism. But Peirce perfects this idea of mediation by the third thing in his logic and semiotics, and based on his dad’s work in mathematics on imaginary numbers Peirce develops the Nonogram which is the modern tensor, and thus grounds mediation in mathematics.
This allows us to go back and explore what Plato called the Worldsoul, which is the two series of numbers 1 2 4 8 and 1 3 9 27. One series is Pascal’s triangle that defines the information infrastructure, and the other is levels of mediation. Peirce places his semiology at the level of three, with the sign mediating between Subject and Object. Later this mediation is seen as the origin of the Subject/Object duality and is seen as Dasein by Heidegger. The level of nine is covered by the Nonogram and is equivalent to the axiomatic platform of Logic, i.e. the four axioms of basic geometry. It is the fifth axiom that gives us problems when we try to leave that stable platform of concepts that are separated from precepts as M. Schlick wants us to do. The fifth axiom throws us into the Meta-system from the restricted economy generated by just the first four axioms and the theorems that can be generated by those. In the Meta-system there are three different geometries that can be produced based on the choice in the fifth axiom that give topological structure to the alternatives in the Meta-system.
At the level 27 we have the mediation of two axiomatic platforms by a third, and this gives us at the same time the underlying structure of reason, and a model of interpenetration.
After that there is a final level of the WorldSoul which is beyond the series that Plato talks about which is comprised of the numbers 16 and 81. This is the level of Matrix Logic of August Stern.
Now, what we have been talking about here is an extension of Hegel’s view of Trialectics, through the additions made by Peirce to traditional logic, as a way to give meaning to Plato’s nebulous idea of the worldsoul. It is basically saying that mediation, which is the hallmark of Hegel’s philosophy, can be formalized as it was by Peirce, and then elaborated in a way that gives the layers of the worldsoul of Plato content and meaning. This kind of interpretation is a kind of Hegelianism because it strives to understand mediation, as a general principe. I develop this idea in my dissertation called Emergent Design (http://emergentdesign) as a way to think about the generalization to even higher levels of the dialectic called quadralectics and pentalectics which I say is the basis for the underlying structure of the dynamics of Design.